We can't go through the hyperstage between tapping the Mox Pearls without destroying all the untapped copies. To gain a layer we have to go through everything below it between the events in the layer, so just creating lots of Mox Pearl tokens gives us just the one layer for producing a lot of white.
But I think we can put a lot of copies of Mimic Vats put a token into play ability on the stack. When we resolve the first we get a Mox Pearl and tap it for white mana. We go through the lower layers and the Hyperstage, destroying the Mimic Vat. When we resolve the next Mimic Vat ability what happens? Do we use last known information to put a Mox Pearl into play? If so, does it matter if the Mox Pearl card has moved zones in between? We can just leave it in exile, but I'd like to know.
Anyway, if we get more Mox Pearl tokens from the abilities after the Mimic Vat is dead already that would be a second layer.
Again, I'm not a rules expert, but yes, I do believe that the ability will survive the destruction of the Mimic Vat that activated it, and also the movement of Mox Pearl between zones after it was activated.
The question is, how do we get lots of Mimic Vat tokens?
Going by the current cards, it seems that Burst of Speed is the only card that permits any Mimic Vat tokens to be created at all.
Mimic Vat's ability only creates a token if the originally exiled card is still in exile as the ability resolves, without having changed zones in the mean time (the Mimic Vat, of course, can change zones or disappear without affecting anything).
World at War as the duplicate spell looks problematic, because it automatically exiles itself on resolution, without having to pay green mana to Bearscape to pull it out.
In that case, I don't think that the Burst of Speed version of the deck can create that extra layer, as we have to move the Mox Pearl out of exile in order to imprint it on another Mimic Vat. I believe that the Scrambleverse version will get the extra layer though, since we can just use a bunch of green mana to untap the same Mimic Vat a bunch of times, leaving the Mox Pearl in exile.
World at War exiling itself shouldn't be a problem, as we would still have to either draw it from the library, or cast it using Spellshift, which itself would require a green mana to get it out of the graveyard.
EDIT: Arh, no the Mutavault plan to make Nomad Mythmaker usable doesn't work. Mutavault would give us the ability to create land tokens with Mimic Vat. Then we no longer need to use Obliterate to get new untapped lands for Elvish Guidance and can just keep converting white mana into green and then using green to untap stuff and get more white.
Without a sorcery that untaps I don't see a way to produce any colored mana from just a sorcery, so I guess the creature land would still work in a version without Scrambleverse.
EDIT2: Nope, the creature land is just bad. Easily goes infinite by enchanting the land token with Elvish Guidance, tapping that for green and then using the green to create more elvish guidance and land tokens. No fancy mana conversions necessary, I don't know why I thought this was save >.< Nomad Mythmaker just doesn't work.
Edit: Nevermind. We could trigger the Underworld Dreams with our own card draw while it is donated and then steal it back and enchant it before it deals the damage. Ugh, changing controllers makes things complicated.
Edit2: Wait, that infinite doesn't actually work. Curiosity requires the damage be to the opponent, presumably the opponent of Curiosity's controller. So It only triggers for us if our opponent has drawn a card first.
Perhaps some gain could be made by going back to Gelectrode, since we are only getting one layer from Repercussion. Then we could possibly do something with +1/+1 counters. I would like to go Curiosity / Chasm Skulker / Ion Storm / Repercussion / Tamanoa[/c], but Repercussion is what we just gave up to be able to access +1/+1 counters. Still, we can buttress Chasm Skulker using Corpsejack Menace, and then, after we activate Ion Storm, we donate it to the opponent to trigger their Tamanoa. (This bit us in the rear before, so it's only fair that we use it to our advantage!) This gains one layer, replacing the layer we lost through Repercussion. The number of card slots is the same as before. But if we get nitpicky, the loss of Repercussion means that Selvala's Enforcer is now worth one layer more, so we can now generate more Finest Hours before the first combat phase. So it is still an improvement.
Here are some possibilities for getting to 20 layers:
Getting those two layers for Mox Pearl is very nice; it would be even better if we could double up on it. If we could find an artifact with casting cost greater than 0 that one could tap and sacrifice to gain black mana, we would gain a layer. Unfortunately, I didn't find any such cards; the closest are Shadowborn Egg and Kaleidostone, which can also draw cards unfortunately.
Another possibility is to switch back to Mortiphobia, so that we could use Wild Research on an instant that gains a layer due to Pyromancer's Goggles. This would require more substantial changes to the ending sequence, but it might be worth it. Looking through the instant cards with X in their casting cost, I didn't find anything really appetizing. Commune with Lava can cast all cards, including Animist's Awakening; Death Denied can only fetch creature cards, which is probably not too useful. What we would like is a card that either cast cards from the library without paying their mana cost, or fetched a permanent from the library or graveyard, but I didn't find any that fit that profile.
That was sort of frustrating, since in both cases the cards I was looking for seem like cards that really should exist!
black mana tapper - 1
some way to transition from that to green mana - 1
Elvish Guidance - 2
Copy Enchantment - 3
Wild Research - 3
white shockland - 4
Boon Reflection - 5
Tamanoa - 6
Squall Line - 7
Wild Research - 7
Barbed Sextant - 9
Genesis Wave - 10
Night Dealings - 11
Boon Reflection - 12
Tamanoa - 13
Underworld Dreams - 14
Curiosity - 15
Underworld Dreams - 16
Pain Magnification - 17
Repercussion - 18
Five Alarm Fire - 19
World at War - 20
So 20 layers, if we can just find some way to transition from black to green.
[EDIT] We can still get 19 layers by replacing Squall Line with Molder, bypassing Tamanoa. This has an extra card slot over the previous version, so perhaps this one is the best currently, unless there is some other problem.
Phantasmal Image doesn't work anyway, since the original dies to easy when entering as a copy of nothing. That in turn might be fixable if we require a Gideon, Ally of Zendikar emblem. Not sure how we would do that, but even if we can acomblish it, the gain is probably not worth it.
EDIT: I accidentally lost earlier edits of this post. Ups.
Anyway I think I got to 20 layers. Riku of Two Reflections should be able to copy Detonate while the blue is too expensive to go infinite with copies of other spells (or Detonate cast from library).
I don't know how to add more than one layer without access to instants though; it would be nice to replace Bearscape with something that exiled just one card at at time, but I don't know of any other than Mortiphobia, which has that discard problem.
Edit: Okay, I think I got 20 layers this time. Invoke the Firemind can only be cast using mana when we have a blue. But if we do we get all the Pyromancer's Goggles copies. We use that to replace Five-Alarm Fire.
When we first retrieve a sorcery we use Hurricane with all flyers removed from the deck and damage to the opponent prevented.