Chaos Warp would give lifegain triggers, psychic battle triggers and a lot of other stuff. The actual spell can then shuffle the Swamp back into the library and reveal it to gain the black mana back.
I'm not sure how we would get multiple lands into play unless we have a way to discard or exile a card from our hand. But we could replace the Swamp with Underground Sea.
I'm not seeing a problem with the deck currently, so I would like to think about possible improvements. The first thing to think about is the possibility of adding stages. It seems that Auriok Bladewarden can easily be replaced by something more narrow (like Rust Tick), but we would have to replace the Korozda Gorgon / Ajani's Pridemate combo, and in particular Devestation seems like it might be very hard to replace with something more narrow. So maybe creatures are out. Possibility Storm gives the possibility of using other card types, but I don't know how to build an Ackermann stage without creature targeting. Also, Possibility Storm may not be compatible with our current build. So maybe no more stages.
If not, then the task becomes to add as many layers onto the end as possible. Unfortunately, I imagine Mirari and Djinn Illuminatus are forbidden, since then we could get multiple black mana per Devastation. So instants/sorceries do not automatically count for layers; also we can cast them again at the cost of a black mana, so we can't get layers that way anyway.
Night Dealings is an old standby; we can transition from there into either opponent life gain or opponent damage. I would like to go
but as you have noticed, with Show and Tell we can have the opponent put a land into play and then destroy it. Chaos Warp is forbidden as you have explained, and Eureka also puts lands into play on the opponent's side. So I'm not seeing an obvious way to get those last few layers.
Unless we manage to get a stage transitions without general creature targeting, I don't see a way to get stages at the end either.
As it is there is a lot that goes infinite even when just trying to add layers. Pain Magnification, Repercussion and Five-Alarm Fire go infinite just by being red spells that we can bounce back to hand to cast again during the basic Ackermann stage.
I don't see a problem with milling our own lands to get them into the graveyard, and from there to the battlefield with Titania, Protector of Argoth. So we can use more lands.
Scrambleverse seems really dangerous, but as it doesn't untap lands I think it is save.
We can't put a limit on the opponents discard, but maybe we can put a limit on putting cards into their library?
We also have 3 colors of mana completely unused and blue is only used for the start, so maybe that can be used to add layers?
Night Dealings won't work when trying to generate black mana with it.
Is there a card other than Mortiphobia to exile instants form graveyards at the cost of some colored mana?
EDIT: I guess I have found another infinite, this time directly involving the stage transition. Essentially Devestation makes the death of Auriok Bladewarden too cheap.
-tap a bladewarden token to put PB triggers on the stack, bounce the original bladewarden and Kaho.
-cast Bladewarden to put BM triggers on the stack, cast Kaho to put BM triggers on the stack.
-tap a Kaho token to cast Devastation, via Spellshift, while it is on the stack do all the stuff to eventuall increase the damage, include bouncing Titania.
-let Devastation resolve, killing Bladewarden and Kaho. Imprint them.
-Cast Titania and other bounced stuff. Get some black to put Spellshift back into the library.
-Make Kaho and Bladewarden tokens, exiling Spellshift with Kaho.
-Get both back using their respective BM triggers.
Repeat.
We can try to move away from Mimic Vat so that the death would be allowed to be cheap. But then we need another way to tie the Devastation cast into the current stage, since we couldn't say only a Kaho token that was just created has the haste necessary to cast the spell.
Getting rid of Mirrorworks and chosing another way to retrieve cards from exile has a slight chance of working. Without it we can not create Mimic Vat tokens, so we can only imprint one of the two creatures in this sequence, since they die at the same time. But my guess is that there is a variation that would go infinite even with that limitation.
We might need to find something other than Devastation though.
Would we need something with indestructible and no other intrusive characteristics, like Darksteel Myr, to be a "holder" for the Splinter Twin while the world blows up, or can Gideon somehow be salvaged to become that holder? I don't see any way of getting back the Splinter Twin short of a Selvala's Enforcer card draw, which is good because getting Splinter Twin back would be able to trigger Staff of the Flame Magus.
On the subject of colored mana -> exiling cards from graveyards, there is Bearscape which produces relatively harmless Bear tokens. It does need a second card in the graveyard each time, somehow.
Bearscape should work fine, we can exile Show and Tell as the second card that needs to be moved from the graveyard to the library.
[EDIT] Now with Bearscape, we can bring Night Dealings and the above sequence back in.
I didn't find many cards with a trigger that sent cards from the graveyard into the library - Quest for Ancient Secrets was about the only one, which gets triggered to easily. For sending cards from graveyard to exile, there is Zombie Cannibal, which triggers on combat damage. So we can finish the sequence with Zombie Cannibal / Finest Hour / World at War.
We can't use Channel due to the donated Exquisite Blood. Without it starting is not that easy.
Using a lot of card space we can add a bunch of big mana producing artifacts and maybe extra copies of Psychic Battle, so that we can bounce more of them before we can start to produce tokens. That would not be very efficient. Any better ideas?
Rasputin Dreamweaver could make 7 mana for free and then another 7 x (# of Psychic Battles) - 2 mana for each +1/+1 counter you can remove to throw at him. That feels intuitively better to me than doing the same thing with mana rocks that tap for 3 at most and need a bunch of nonsense with March of the Machine bounces to activate multiple times, but then again, this deck has officially jumped of the intuitive cliff...
Side note: I really wanted to say something with Doubling Cube, but that can generate colored mana.
P.P.S. Energy Tap + Draco seems like a fun time. Maybe not here since it has no scaling factor at all, but as a mostly EDH player, I suddenly feel like making a big mana cost deck.
Edit again: Assuming Cephalid Shrine and Bloodbond March can be involved, Rasputin would make way more mana than a mana rock. As long as he doesn't go infinite, of course.
Since there's actually a sizable amount of breathing room, I was going to suggest Grip of Chaos to nest Psychic Battles inside it, but of course that is a red card, and it is way too easy to bounce.
Speaking of red cards, World at War and Scrambleverse both look problematic. In particular, a Spellweaver Helix imprint of Show and Tell + Scrambleverse provides easy untaps for everything in addition to the lifegain trigger. If Donate is an unacceptable substitute for Scrambleverse due to the targeting, there's always Cultural Exchange as an option, combined with something like Hunted Phantasm that can guarantee large numbers of tokens for the opponent.
Scrambleverse and World at War gain life (and Scrambleverse gains untaps) but neither gets that precious green mana back, so I don't think that either go infinite.
Does Enter the Infinite go infinite? Without Mirari / Djinn Illuminatus it can't draw itself, so that's not a problem. If we imprint it on a Spellweaver Helix along with a Show and Tell, we can cast Spellshift, find the other Show and Tell and cast it, and then cast Enter the Infinite. Before the Enter the Infinite resolves, we can put Spellshift and Show and Tell back in the library at the cost of a green mana, along with Jokulhaups - no, that's too good. Too bad.
What about Primal Surge? It can only fetch permanents, but that does include Tropical Island. It can also put Auriok Bladewarden back on the battlefield, but that doesn't generate any additional targeting by itself. So I don't see an infinite, but I'm not sure.
[EDIT] Primal Surge can only retrieve Tropical Island if it is off the battlefield, which requires a Jokulhaups. So I'm pretty sure it doesn't go infinite.
I guess we still need colorless mana in addition to Primal Surge - is Rasputin Dreamweaver enough?
[EDIT 2] Mana Echoes would be better, but it's red...
Yeah, the Primal Surge is just meant to be an extra card that helps the start a little, not a replacement for Selvala's Enforcer.
With Jokulhaups not allowing any benefit from the destruction of creatures, there seems to be a slight glimmer of possibility of future creature stages. The only impediment now seems to be the Korozda Gorgon / Ajani's Pridemate / Staff of the Flame Magus combo; if that can be replaced by something more narrow, we could have subsequent stages.
The most likely target seems to be artifacts. I haven't been able to find anything though. There doesn't seem to be much else that triggers off of life gain, except card draw from Drogskol Reaver or Well of Lost Dreams. I'm not sure whether card draw goes infinite immediately, but anyway it probably messes with subsequent stages. I didn't see many alternatives for removing +1/+1 counters that didn't come from cards that came with +1/+1 counters. As for alternatives for casting a red spell, there are cards like Baleful Liege that damage a target player; I'm not sure what to do with that. There's also Tibor and Lumia which damages each creature without flying, which could destroy creatures without flying. Unfortunately, getting a batch of destruction triggers is not enough to kick off a stage; otherwise we could follow that with flying creature stages. Oh well.
I still think there is a possibility for subsequent stages though.
First we put at least five Oath of Gideons on the battlefield. Then we play Teferi and activate his ultimate to get the emblem. Then we can use Xenagos to get lots of green mana, destroy it with Dreadbore, exile it with Bearscape, put it back in the library with Riftsweeper, then put it in our hand with Night Dealings. It's somewhat profligate to use five cards to get one layer, but we do have the space...
All hasty versions of Staff of the Flame Magus get destroyed by Jokulhaups and we can't get new hasty tokens without the staff dying, at which point we can't get it back. The deck still works with just one lifegain trigger, since we can still get a lot of +1/+1 counters from that, but I think Kor Firewalker is just better. Although that would probably go infinite by donating them now that I think about it.
For an additional layer unter Night Dealings I found Elvish Guidance. It can only enchant lands, so it will die from each Jokulhaups. The cheapest way to reuse it after all lands are tapped is to destroy the lands and retrieve Elvish Guidance with Night Dealings. Doing that enables the Night Dealings to generate X green mana. Seems a bit easier than the planeswalker plan.
EDIT: Copy Enchantment would allow us to create more copys of Elvish Guidance before we tap the land, and then the one tapping gives X triggers, that all add X mana. Another layer.
I don't think Copy Enchantment goes infinite. The Elvish Guidance still dies, and making copies of Splinter Twin doesn't seem useful when we can just move it.
Yes, Elvish Guidance is much simpler! We will need to add an Elf, since we can't really put a bunch of Selvala's Enforcers on the battlefield.
It occurs to me that we could replace Underground Sea by either Fungal Reaches or Saltcrusted Steppe; both of those would also generate one green per destruction and retrieval by Titania, Protector of Argoth. The difference is that we don't tap them to generate the mana, so they won't be affected by Mana Reflection. This allows us to stick in Mana Reflection and possibly gain layers for colors more easily. We have to use tapping permanents though; I'm not quite sure how to put those above the hyperstage.
[EDIT] Can you explain how we get lots of Elvish Guidances using Copy Enchantment? We can make a copy of Copy Enchantment using Splinter Twin, but by then it's too late to turn the original Copy Enchantment into an Elvish Guidance, so I don't see how to make progress.
We can use white mana and Nomad Mythmaker to retrieve Elvish Guidance instead of Night Dealings. So the task for the Nightdealings is to retrieve something, that can make a lot of white. Mox Diamond is a permanent that can tap for white, but only if we can discard a land. That is expensive enough as a requirement here. Night Dealings can't search up a land directly, but it can get say Fiery Fall. Mox Diamond also excludes using other colors later, so maye there are other options?
So for now Night dealings gets Fiery Fall, gets an Island, gets discarded for Mox Diamond. Taps for X white mana. Each white mana recovers Elvish Guidance. Which is one layer.
I was hoping to use Nature's Will and a tappedland that can produce a new, more expensive color to complete the opponents graveyard to library cycle with an additional layer, but I did not find effects in the right color for that. Black is usable, but then we need to change Night Dealings for something else.
I think I found a good idea, although it may be to simple to be correct. Without Glorious Anthem, we cannot bounce 0 cost artifacts, so something like Mox Pearl can be used once and then has to be redrawn again. We can fetch it using Night Dealings for two black mana only. So now we need something that generates black mana. I think Mox Diamond / Fiery Fall would work, but even simpler is to use something like Astrolabe, as that has to be tapped to be used, so making copies using Splinter Twin doesn't help. So I think Astrolabe also has to be redrawn to be reused, this time using theft counters from Night Dealings. So if my count is correct, that's three additional layers, for F_{w^2 + 10} (3). Progress!
So far we've used green, white and black. Red mana is sort of messed up by Fungal Reaches, but we can still use blue mana, switching from Show and Tell to Eureka if necessary.
Can we get that additional layer using Clever Impersonator instead of Copy Enchantment? For Clever Impersonator we can simply use Mimic Vat tokens. Hmm, but I guess Clever Impersonator can also copy Auriok Bladewarden, leading to extra hasted token copies. Oh well.
All those artifact mana creators don't work with Scrambleverse as that can untap them for essentially just a green. Luckily we have other options for donation, as SadisticMystic pointed out before. Donate should still be save.
Edit: Actually Mox Pearl would be save, as the only way to convert white into green eventually requires Jokulhaups after all lands are tapped. That destroys the Mox and we need to redraw it.
So if we have no permanents that can produce green whenn we untap them, we can actually use X green mana and a Copy Enchantment imprinted on Mimic Vat to produce X Elvish Guidance token. At this point that it not worth a layer as we can't use white to retrieve the Copy Enchantment and the Mimic Vat that has it imprinted dies during the Hyperstage. I also don't see how we would get the black without creating green via untap. The requirement to sacrifce the Astrolabe doesn't help since we can create tapped tokens easily.
Edit2: The Zombie Cannibal layer doesn't work, as all triggers go on the stack at the same time. Psychic Battle triggers only after that, so we can exile at most 60 different targets. Ghastlord of Fugue would be a working replacement. That also skips the part where we have to make the opponent discard. They can't empty their hand with Show and Tell to dodge the exile from hand since we will always counter that spell after the one time in the setup.
That Copy Enchantment combo looks interesting, but I don't see a way right now to make a gain from it.
I believe I have found a good alternative Jokulhaups trigger: Instead of using "whenever you cast a red spell", we use "whenever you cast an instant or sorcery spell". So we can use Gelectrode for example, or Korozda Gorgon / Pyre Hound. The advantage is that we do not nix red permanents, or our life total / life gain. A major difference is that now casting Spellshift will trigger Gelectrode or Pyre Hound three times rather than once, but all the gain we make will be wiped away by the board clear anyway (except for the enchantments that save our progress), so I think it should be okay.
I'm a little disappointed that I was only able to manange four layers in between Night Dealings and Pain Magnification even with our own life to help out, but the extra gain from Pain Magnfication on gets us two more layers, for F_{w^2+12}(3). (Please check this.)
I don't think Gelectrode works. The problem is that we get some of the untaps resolved before we put Jokulhaups on the stack. So that part helps out the current Ackermann stage instead of the one below the marker. So the stage can restart itself which goes infinite.
And I don't think Spellshift countering the Show and Tell from the last cast works out, as that has to be cleared from the stack already before we want to cast the next Jokulhaups.
EDIT: Hmm, while we resolve the first batch of untaps we have the Spellshift cast on the stack as marker, so those only help the lower stage. When we resolve Spellshift to cast Show and Tell we trigger poth Spellweaver Helix and another batch of untaps. Untap trigger that we resolve before the helix are on the lower side of the marker (which currently is the Helix trigger). Untap trigger that we try to resolve after the helix fail, since the Jokulhaups has destroyed the Gelectrodes. This might work after all. Nice.
EDIT2: That build can't have a second instant, as that would allow us to move the second instant with the same Bearscape activation that moves the Spellshift. But then we can use Kaho to cast that second instant to refresh the current stage.
The reason I wanted a second instant was so that we could use the Island we needed anyway, but that's fine, we can use a sorcery - return of Appetite for Brains!
[EDIT] Concerning the Copy Enchantment combo, we can use Crystal Chimes to retrieve both Copy Enchantment and Elvish Guidance. If we start with X green mana, we can cast X Scrambleverses; each one can untap a bunch of Crystal Chimes; we can sacrifice the Crystal Chimes to put a bunch of abilities on the stack, and each one can return Copy Enchantment and Elvish Guidance. So is it four layers? It's a little hinky, so I'm not sure. If so, it is one more layer than the Mox Pearl / Barbed Sextant combo, provided we hook Crystal Chimes into Night Dealings. Or, we could transition to Argivian Archaeologist, and then try to find some way to generate white mana. (Unfortunately, Argivian Archaeologist nixes Mox Pearl and other artifacts.)
Whenever we retrieve Crystal Chimes we can create X tokens, untap them and put the ability on the stack for all of them. Putting additional untaps on the stack doesn't help, since the Crystal Chimes are destroyed during the Hyperstage.
Every time a Crystal Chimes ability is resolved we get Elvish Guidance and Copy Enchantment. We can create X Elvish Guidance tokens by untapping a Mimic Vat using all our green mana. Those tokens then all put one trigger on the stack when we tap the land.
Each Elvish Guidance trigger gives us X green Mana which we use to go through the Hyperstage.
I count 3 layers, the same as X green Mana per white mana, X white mana per black mana, X black mana per retrieval.
I'm not sure how we would get multiple lands into play unless we have a way to discard or exile a card from our hand. But we could replace the Swamp with Underground Sea.
I'm not seeing a problem with the deck currently, so I would like to think about possible improvements. The first thing to think about is the possibility of adding stages. It seems that Auriok Bladewarden can easily be replaced by something more narrow (like Rust Tick), but we would have to replace the Korozda Gorgon / Ajani's Pridemate combo, and in particular Devestation seems like it might be very hard to replace with something more narrow. So maybe creatures are out. Possibility Storm gives the possibility of using other card types, but I don't know how to build an Ackermann stage without creature targeting. Also, Possibility Storm may not be compatible with our current build. So maybe no more stages.
If not, then the task becomes to add as many layers onto the end as possible. Unfortunately, I imagine Mirari and Djinn Illuminatus are forbidden, since then we could get multiple black mana per Devastation. So instants/sorceries do not automatically count for layers; also we can cast them again at the cost of a black mana, so we can't get layers that way anyway.
Night Dealings is an old standby; we can transition from there into either opponent life gain or opponent damage. I would like to go
Night Dealings
Horizon Chimera (donated using Scrambleverse)
Boon Reflection
Selvala's Enforcer
Pain Magnification
Repercussion
Five-Alarm Fire
World at War
but as you have noticed, with Show and Tell we can have the opponent put a land into play and then destroy it. Chaos Warp is forbidden as you have explained, and Eureka also puts lands into play on the opponent's side. So I'm not seeing an obvious way to get those last few layers.
Still, we should have at least F_{w^2+3}(X).
As it is there is a lot that goes infinite even when just trying to add layers.
Pain Magnification, Repercussion and Five-Alarm Fire go infinite just by being red spells that we can bounce back to hand to cast again during the basic Ackermann stage.
I don't see a problem with milling our own lands to get them into the graveyard, and from there to the battlefield with Titania, Protector of Argoth. So we can use more lands.
Scrambleverse seems really dangerous, but as it doesn't untap lands I think it is save.
We can't put a limit on the opponents discard, but maybe we can put a limit on putting cards into their library?
We also have 3 colors of mana completely unused and blue is only used for the start, so maybe that can be used to add layers?
Night Dealings won't work when trying to generate black mana with it.
Is there a card other than Mortiphobia to exile instants form graveyards at the cost of some colored mana?
Good idea on using colors, no ideas yet.
Tentative start: assuming we replace Mortiphobia with Purify the Grave:
Night Dealings
Boon Reflection
Tamanoa
Underworld Dreams
Consecrated Sphinx
Selvala's Enforcer
that would get F_{w^2+5}(X) - but no, Tamanoa is a red permanent as well. Anything that can replace it?
[EDIT] We can replace Tamanoa with Exquisite Blood, then use Vampiric Touch to damage the opponent.
EDIT: I guess I have found another infinite, this time directly involving the stage transition. Essentially Devestation makes the death of Auriok Bladewarden too cheap.
-tap a bladewarden token to put PB triggers on the stack, bounce the original bladewarden and Kaho.
-cast Bladewarden to put BM triggers on the stack, cast Kaho to put BM triggers on the stack.
-tap a Kaho token to cast Devastation, via Spellshift, while it is on the stack do all the stuff to eventuall increase the damage, include bouncing Titania.
-let Devastation resolve, killing Bladewarden and Kaho. Imprint them.
-Cast Titania and other bounced stuff. Get some black to put Spellshift back into the library.
-Make Kaho and Bladewarden tokens, exiling Spellshift with Kaho.
-Get both back using their respective BM triggers.
Repeat.
We can try to move away from Mimic Vat so that the death would be allowed to be cheap. But then we need another way to tie the Devastation cast into the current stage, since we couldn't say only a Kaho token that was just created has the haste necessary to cast the spell.
Getting rid of Mirrorworks and chosing another way to retrieve cards from exile has a slight chance of working. Without it we can not create Mimic Vat tokens, so we can only imprint one of the two creatures in this sequence, since they die at the same time. But my guess is that there is a variation that would go infinite even with that limitation.
We might need to find something other than Devastation though.
On the subject of colored mana -> exiling cards from graveyards, there is Bearscape which produces relatively harmless Bear tokens. It does need a second card in the graveyard each time, somehow.
Bearscape should work fine, we can exile Show and Tell as the second card that needs to be moved from the graveyard to the library.
[EDIT] Now with Bearscape, we can bring Night Dealings and the above sequence back in.
I didn't find many cards with a trigger that sent cards from the graveyard into the library - Quest for Ancient Secrets was about the only one, which gets triggered to easily. For sending cards from graveyard to exile, there is Zombie Cannibal, which triggers on combat damage. So we can finish the sequence with Zombie Cannibal / Finest Hour / World at War.
So, the deck so far:
2 Opalescence
3 Psychic Battle
4 Cowardice
5 Horobi, Death's Wail
6 Bloodbond March
7 Cephalid Shrine
8 Glorious Anthem
9 Mana Crypt
10 Creepy Doll
11 March of the Machines
12 Selvala's Enforcer
13 Mindshrieker
14 Mimic Vat
15 Omniscience
16 Leyline of Anticipation
17 Riftsweeper
19 Crown of the Ages
20 Auriok Bladewarden
21 Korozda Gorgon
22 Ajani's Pridemate
23 Staff of the Flame Magus
24 Jokulhaups
25 Spellweaver Helix
26 Kaho, Minamo Historian
27 Spellshift
28 Show and Tell
29 Show and Tell
30 Battle Screech
31 Bearscape
33 Titania, Protector of Argoth
34 Channel
35 Mox Jet
36 Night Dealings
37 Boon Reflection
38 Exquisite Blood
39 Underworld Dreams
40 Consecrated Sphinx
41 Zombie Cannibal
42 Finest Hour
43 World at War
44 Scrambleverse
This should get about F_{w^2 + 7} (3).
We can't use Channel due to the donated Exquisite Blood. Without it starting is not that easy.
Using a lot of card space we can add a bunch of big mana producing artifacts and maybe extra copies of Psychic Battle, so that we can bounce more of them before we can start to produce tokens. That would not be very efficient. Any better ideas?
Side note: I really wanted to say something with Doubling Cube, but that can generate colored mana.
P.P.S. Energy Tap + Draco seems like a fun time. Maybe not here since it has no scaling factor at all, but as a mostly EDH player, I suddenly feel like making a big mana cost deck.
Edit again: Assuming Cephalid Shrine and Bloodbond March can be involved, Rasputin would make way more mana than a mana rock. As long as he doesn't go infinite, of course.
Speaking of red cards, World at War and Scrambleverse both look problematic. In particular, a Spellweaver Helix imprint of Show and Tell + Scrambleverse provides easy untaps for everything in addition to the lifegain trigger. If Donate is an unacceptable substitute for Scrambleverse due to the targeting, there's always Cultural Exchange as an option, combined with something like Hunted Phantasm that can guarantee large numbers of tokens for the opponent.
Does Enter the Infinite go infinite? Without Mirari / Djinn Illuminatus it can't draw itself, so that's not a problem. If we imprint it on a Spellweaver Helix along with a Show and Tell, we can cast Spellshift, find the other Show and Tell and cast it, and then cast Enter the Infinite. Before the Enter the Infinite resolves, we can put Spellshift and Show and Tell back in the library at the cost of a green mana, along with Jokulhaups - no, that's too good. Too bad.
What about Primal Surge? It can only fetch permanents, but that does include Tropical Island. It can also put Auriok Bladewarden back on the battlefield, but that doesn't generate any additional targeting by itself. So I don't see an infinite, but I'm not sure.
If Primal Surge, doesn't work, I do like the idea of Rasputin Dreamweaver, or Energy Tap plus Draco if more is needed. I was thinking about alternatives to Selvala's Enforcer, like Temple Bell or Words of Wisdom, but those don't seem to be as good.
[EDIT] Primal Surge can only retrieve Tropical Island if it is off the battlefield, which requires a Jokulhaups. So I'm pretty sure it doesn't go infinite.
I guess we still need colorless mana in addition to Primal Surge - is Rasputin Dreamweaver enough?
[EDIT 2] Mana Echoes would be better, but it's red...
[EDIT 3] Storm Herd and Ashnod's Altar would be better than Energy Tap and Draco.
Start with Tropical Island, Mana Crypt, Show and Tell into Omniscience.
Then Consecrated Sphinx, Selvala's Enforcer draws 3 and produces one +1/+1 counter.
Play Rasputin Dreamweaver, Cowardice, Psychic Battle, Korozda Gorgon. We get 7 mana.
We can now spend 2 mana and the +1/+1 counter to bounce both Selvala's Enforcer and Rasputin Dreamweaver, drawing 3 cards and replenishing the +1/+1 counter as well as generating 7 mana.
The only question is how fast we can escalate, but since the cards in opponents library are not our final limiter that should not matter that much.
With Rasputin to produce colorless we don't need a Glorious Anthem anymore as Mana Crypt is allowed to die.
With Primal Surge instead of Selvala's Enforcer I see some problems with generating enough +1/+1 counters to produce any tokens in the start.
With Jokulhaups not allowing any benefit from the destruction of creatures, there seems to be a slight glimmer of possibility of future creature stages. The only impediment now seems to be the Korozda Gorgon / Ajani's Pridemate / Staff of the Flame Magus combo; if that can be replaced by something more narrow, we could have subsequent stages.
The most likely target seems to be artifacts. I haven't been able to find anything though. There doesn't seem to be much else that triggers off of life gain, except card draw from Drogskol Reaver or Well of Lost Dreams. I'm not sure whether card draw goes infinite immediately, but anyway it probably messes with subsequent stages. I didn't see many alternatives for removing +1/+1 counters that didn't come from cards that came with +1/+1 counters. As for alternatives for casting a red spell, there are cards like Baleful Liege that damage a target player; I'm not sure what to do with that. There's also Tibor and Lumia which damages each creature without flying, which could destroy creatures without flying. Unfortunately, getting a batch of destruction triggers is not enough to kick off a stage; otherwise we could follow that with flying creature stages. Oh well.
I still think there is a possibility for subsequent stages though.
[EDIT] I believe we can add a layer by putting in Xenagos, the Reveler, Teferi, Temporal Archmage, Oath of Gideon, Mirror Gallery, and Dreadbore.
First we put at least five Oath of Gideons on the battlefield. Then we play Teferi and activate his ultimate to get the emblem. Then we can use Xenagos to get lots of green mana, destroy it with Dreadbore, exile it with Bearscape, put it back in the library with Riftsweeper, then put it in our hand with Night Dealings. It's somewhat profligate to use five cards to get one layer, but we do have the space...
For an additional layer unter Night Dealings I found Elvish Guidance. It can only enchant lands, so it will die from each Jokulhaups. The cheapest way to reuse it after all lands are tapped is to destroy the lands and retrieve Elvish Guidance with Night Dealings. Doing that enables the Night Dealings to generate X green mana. Seems a bit easier than the planeswalker plan.
EDIT: Copy Enchantment would allow us to create more copys of Elvish Guidance before we tap the land, and then the one tapping gives X triggers, that all add X mana. Another layer.
I don't think Copy Enchantment goes infinite. The Elvish Guidance still dies, and making copies of Splinter Twin doesn't seem useful when we can just move it.
It occurs to me that we could replace Underground Sea by either Fungal Reaches or Saltcrusted Steppe; both of those would also generate one green per destruction and retrieval by Titania, Protector of Argoth. The difference is that we don't tap them to generate the mana, so they won't be affected by Mana Reflection. This allows us to stick in Mana Reflection and possibly gain layers for colors more easily. We have to use tapping permanents though; I'm not quite sure how to put those above the hyperstage.
[EDIT] Can you explain how we get lots of Elvish Guidances using Copy Enchantment? We can make a copy of Copy Enchantment using Splinter Twin, but by then it's too late to turn the original Copy Enchantment into an Elvish Guidance, so I don't see how to make progress.
Hmm, you are right, Copy Enchantment does not produce aura tokens in this setup.
But Mana Reflection for the ending sequence is very useful.
We can use white mana and Nomad Mythmaker to retrieve Elvish Guidance instead of Night Dealings. So the task for the Nightdealings is to retrieve something, that can make a lot of white. Mox Diamond is a permanent that can tap for white, but only if we can discard a land. That is expensive enough as a requirement here. Night Dealings can't search up a land directly, but it can get say Fiery Fall. Mox Diamond also excludes using other colors later, so maye there are other options?
So for now Night dealings gets Fiery Fall, gets an Island, gets discarded for Mox Diamond. Taps for X white mana. Each white mana recovers Elvish Guidance. Which is one layer.
I was hoping to use Nature's Will and a tappedland that can produce a new, more expensive color to complete the opponents graveyard to library cycle with an additional layer, but I did not find effects in the right color for that. Black is usable, but then we need to change Night Dealings for something else.
So far we've used green, white and black. Red mana is sort of messed up by Fungal Reaches, but we can still use blue mana, switching from Show and Tell to Eureka if necessary.
Can we get that additional layer using Clever Impersonator instead of Copy Enchantment? For Clever Impersonator we can simply use Mimic Vat tokens. Hmm, but I guess Clever Impersonator can also copy Auriok Bladewarden, leading to extra hasted token copies. Oh well.
Edit: Actually Mox Pearl would be save, as the only way to convert white into green eventually requires Jokulhaups after all lands are tapped. That destroys the Mox and we need to redraw it.
So if we have no permanents that can produce green whenn we untap them, we can actually use X green mana and a Copy Enchantment imprinted on Mimic Vat to produce X Elvish Guidance token. At this point that it not worth a layer as we can't use white to retrieve the Copy Enchantment and the Mimic Vat that has it imprinted dies during the Hyperstage. I also don't see how we would get the black without creating green via untap. The requirement to sacrifce the Astrolabe doesn't help since we can create tapped tokens easily.
Edit2: The Zombie Cannibal layer doesn't work, as all triggers go on the stack at the same time. Psychic Battle triggers only after that, so we can exile at most 60 different targets. Ghastlord of Fugue would be a working replacement. That also skips the part where we have to make the opponent discard. They can't empty their hand with Show and Tell to dodge the exile from hand since we will always counter that spell after the one time in the setup.
I believe I have found a good alternative Jokulhaups trigger: Instead of using "whenever you cast a red spell", we use "whenever you cast an instant or sorcery spell". So we can use Gelectrode for example, or Korozda Gorgon / Pyre Hound. The advantage is that we do not nix red permanents, or our life total / life gain. A major difference is that now casting Spellshift will trigger Gelectrode or Pyre Hound three times rather than once, but all the gain we make will be wiped away by the board clear anyway (except for the enchantments that save our progress), so I think it should be okay.
Of course, we cannot have Battle Screech anymore. Can we not simply use Spellshift to counter the previously cast Show and Tell? If not, we can always use Izzet Guildmage and some cheap instant sorcery.
So, the prospective deck:
2 Opalescence
3 Psychic Battle
4 Cowardice
5 Horobi, Death's Wail
6 Bloodbond March
7 Cephalid Shrine
8 Rasputin Dreamweaver
9 Mana Crypt
10 Creepy Doll
11 March of the Machines
12 Selvala's Enforcer
13 Mindshrieker
14 Mimic Vat
15 Omniscience
16 Leyline of Anticipation
17 Riftsweeper
19 Crown of the Ages
20 Gelectrode
21 Jokulhaups
22 Spellweaver Helix
23 Kaho, Minamo Historian
24 Spellshift
25 Show and Tell
26 Show and Tell
27 Aura Graft
28 Izzet Guildmage
29 Bearscape
30 Fungal Reaches
31 Island
32 Titania, Protector of Argoth
33 Mana Reflection
34 Elvish Guidance
35 Nomad Mythmaker
36 Mox Pearl
37 Barbed Sextant
38 Night Dealings
39 Boon Reflection
40 Tamanoa
41 AEther Sting
42 Confessor
43 Pain Magnfication
44 Repercussion
45 Five-Alarm Fire
46 Finest Hour
47 World at War
49 Primal Surge
50 Floating-Dream Zubera
51 Thought Reflection
I'm a little disappointed that I was only able to manange four layers in between Night Dealings and Pain Magnification even with our own life to help out, but the extra gain from Pain Magnfication on gets us two more layers, for F_{w^2+12}(3). (Please check this.)
Does this work?
And I don't think Spellshift countering the Show and Tell from the last cast works out, as that has to be cleared from the stack already before we want to cast the next Jokulhaups.
EDIT: Hmm, while we resolve the first batch of untaps we have the Spellshift cast on the stack as marker, so those only help the lower stage. When we resolve Spellshift to cast Show and Tell we trigger poth Spellweaver Helix and another batch of untaps. Untap trigger that we resolve before the helix are on the lower side of the marker (which currently is the Helix trigger). Untap trigger that we try to resolve after the helix fail, since the Jokulhaups has destroyed the Gelectrodes. This might work after all. Nice.
EDIT2: That build can't have a second instant, as that would allow us to move the second instant with the same Bearscape activation that moves the Spellshift. But then we can use Kaho to cast that second instant to refresh the current stage.
The reason I wanted a second instant was so that we could use the Island we needed anyway, but that's fine, we can use a sorcery - return of Appetite for Brains!
[EDIT] Concerning the Copy Enchantment combo, we can use Crystal Chimes to retrieve both Copy Enchantment and Elvish Guidance. If we start with X green mana, we can cast X Scrambleverses; each one can untap a bunch of Crystal Chimes; we can sacrifice the Crystal Chimes to put a bunch of abilities on the stack, and each one can return Copy Enchantment and Elvish Guidance. So is it four layers? It's a little hinky, so I'm not sure. If so, it is one more layer than the Mox Pearl / Barbed Sextant combo, provided we hook Crystal Chimes into Night Dealings. Or, we could transition to Argivian Archaeologist, and then try to find some way to generate white mana. (Unfortunately, Argivian Archaeologist nixes Mox Pearl and other artifacts.)
Every time a Crystal Chimes ability is resolved we get Elvish Guidance and Copy Enchantment. We can create X Elvish Guidance tokens by untapping a Mimic Vat using all our green mana. Those tokens then all put one trigger on the stack when we tap the land.
Each Elvish Guidance trigger gives us X green Mana which we use to go through the Hyperstage.
I count 3 layers, the same as X green Mana per white mana, X white mana per black mana, X black mana per retrieval.
Edit: I think I see a continuation layer when using Argivian Archaeologist. We get X white mana whenever we tap Selesnya Guildgate. But to untap that in the first place we need to search for Teferi, Temporal Archmage with Night Dealings.
Dreadbore, Oath of Gideon and Mirror Gallery are needed for support. Teferi's first ability can find Teferi, but I that doesn't give any advantage, so it shouldn't create infinite damage.
What about if we get more adventurous:
Argivian Archaeologist
Adarkar Wastes
Boon Reflection
Tamanoa
Repercussion
Chandra, Pyromaster
Night Dealings
That's three more layers than the above, but we use up our life along the way.
A possible continuation:
Night Dealings
Boon Reflection
Tamanoa
Underworld Dreams
Consecrated Sphinx
Ghastlord of Fugue
Finest Hour
World at War
That's 14 layers, if I'm not mistaken.
[EDIT] Replace Adarker Wastes with Mana Confluence.
The same thing is in the previous sequence. We can remove the Repercussion layer to fix it. So both sequences lose a layer.
As long as we can produce more than one green from permanents Primal Surge seems to go infinite. We should just start without it.