I like the idea of Naru as a combo deck for Brawl, but I don't agree with the way you've built her. I think the key here is redundancy, as well as killing the turn you combo off before anybody gets to untap.
We then have some cheap bounce/protection/card draw/value engines while we build up the mana. The only irreplaceable piece is Naru... and she's always hanging out in the command zone! In the event that a combo gets broken up and strands her on the battlefield, either bounce spell, Release to the Wind, Baral’s Expertise, or Vizier making a copy and killing the original can all get her back where she belongs.
It's possible I'm a few cards off here and there, but I think the general strategy is significantly more powerful than building an entire deck around Illusionist's Stratagem that still isn't infinite when it goes off. Remember, that card draw isn't optional! (Also, note that you need to have at least two targets initially, since copies can’t change number of targets!)
Although I'm not sure how strong this will be in multiplayer, a similar list headed by Baral is probably one of the best things you can do in 1v1. There's a reason he's banned in 1v1 Commander.
Note that when I say the combo is a lot cheaper with Paradox Engine or Mirage Mirror in play, I mean a *lot* cheaper. With Mirage Mirror, it's 12 mana to go infinite (10 if you EoT), with Saheeli it's 10, and with paradox engine you can probably do it from 7 with relative ease. That still might not be worth it, but once you're on 10+ artifact tutors / search effects, I really like having an infinite combo available.
That said, if you want to combo off with Cogwork, you might be better off just playing with Saheeli as your commander to ensure the free copy on demand, and then just playing a mostly-blue counterspell / cantrip deck that goes off for infinite whenever the coast is clear. Or maybe even going mono-blue with Padeem as your commander.
Is there a reason you're not playing the natural artifact infinite combo?
Powerstone Shard goes infinite and kills the table with Cogwork Assembler and 17 mana- which this deck seems like it could reliably generate.
Cast or Whir both Powerstone and Cogwork into play
Copy Powerstone with Cogwork (7 mana spent)
Copy Powerstone with Cogwork (14 mana spent)
Tap two Powerstones for 3, copy one with Cogwork (15 mana spent)
Tap two Powerstones for 8, copy one with Cogwork (15 mana spent, float 1)
Tap the last Powerstone for 5, copy it with Cogwork (16 mana spent)
Tap Powerstone for 6, copy it with Cogwork (17 mana spent)
Tap Powerstone for 7, copy it with Cogwork (17 mana spent)
Tap Powerstone for 8, copy it with Cogwork (17 mana spent, float 1)
You can keep doing this from here generating infinite mana until you decide to copy Cogwork with itself infinite times and attack with infinite 2/3s.
The reason I really like this combo is that all three pieces - Powerstone, Cogwork, and Mirror - can be tutored with Trophy Mage, Whir of Invention, and Inventors' Fair, which makes it very reliable. Also, not having Glint-Nest Crane in here seems like an oversight; it's a ridiculously efficient cantrip.
My take looks more like Magical Christmas Land.
4 Naru Meha, Master Wizard
Creatures: 10
2 Baral, Chief of Compliance
2 Diligent Excavator
2 Glint-Nest Crane
2 Vodalian Arcanist
3 Nimble Obstructionist
3 Sailor of Means
3 Trophy Mage
4 Vizier of Many Faces
5 Prosperous Pirates
6 Torrential Gearhulk
Artifacts: 9
1 Silent Gravestone
2 Thaumatic Compass
2 Treasure Map
3 Bontu's Monument
3 Cultivator's Caravan
3 Orazca Relic
4 Aetherflux Reservoir
4 Primal Amulet
5 Gilded Lotus
1 Opt
1 Spell Pierce
2 Blink of an Eye
2 Negate
2 Pull from Tomorrow
3 Release to the Wind
3 Supreme Will
3 Unwind
3 Whir of Invention
4 Glimmer of Genius
4 Hieroglyphic Illumination
4 Illusionist's Stratagem
5 Baral's Expertise
5 Spell Swindle
6 Saheeli's Artistry
2 Search for Azcanta
Lands: 24
1 Arch of Orazca
1 Desert of the Mindful
1 Field of Ruin
1 Inventors' Fair
1 Ipnu Rivulet
1 Memorial to Genius
1 Scavenger Grounds
1 Zhalfirin Void
16 Island
The deck features the following combos with Naru:
Release to the Wind + Diligent Excavator = Infinite Mill
Release to the Wind + Bontu's Monument = Infinite Drain
Release to the Wind + Aetherflux Reservoir = Infinite Lifegain + Infinite Damage
Baral's Expertise + Diligent Excavator = Infinite Mill
Baral's Expertise + Bontu's Monument = Infinite Drain
Baral's Expertise + Aetherflux Reservoir = Infinite Lifegain + Infinite Damage
Illusionist's Stratagem + Sailor of Means + (any other creature) = Draw your deck with enough mana to switch to a real infinite combo
Illusionist's Stratagem + Prosperous Pirates + (any other creature) = Draw your deck with enough mana to switch to a real infinite combo
Illusionist's Stratagem + Cultivator's Caravan + (one other creature that can crew or two other creatures) = Draw your deck with enough mana to switch to a real infinite combo
Saheeli's Artistry + (one creature and one artifact on the battlefield) = Infinite Copies of every artifact and creature on the battlefield, possibly feeding into one of the above combos
There are also the lesser combos of Illusionist's Stratagem + Vizier of Many Faces or Torrential Gearhulk possibly feeding into one of the above.
Since all of our infinite combos go infinite off either Cultivator's Caravan or Bontu's Monument, Trophy Mage and Whir of Invention can always find a combo piece, and Glint-Nest Crane often can too. (It's around 60% to hit a card, which isn't amazing, but it's pretty good to staple onto a 1/3 flying blocker)
We then have some cheap bounce/protection/card draw/value engines while we build up the mana. The only irreplaceable piece is Naru... and she's always hanging out in the command zone! In the event that a combo gets broken up and strands her on the battlefield, either bounce spell, Release to the Wind, Baral’s Expertise, or Vizier making a copy and killing the original can all get her back where she belongs.
It's possible I'm a few cards off here and there, but I think the general strategy is significantly more powerful than building an entire deck around Illusionist's Stratagem that still isn't infinite when it goes off. Remember, that card draw isn't optional! (Also, note that you need to have at least two targets initially, since copies can’t change number of targets!)
Although I'm not sure how strong this will be in multiplayer, a similar list headed by Baral is probably one of the best things you can do in 1v1. There's a reason he's banned in 1v1 Commander.
What a Jerk
That said, if you want to combo off with Cogwork, you might be better off just playing with Saheeli as your commander to ensure the free copy on demand, and then just playing a mostly-blue counterspell / cantrip deck that goes off for infinite whenever the coast is clear. Or maybe even going mono-blue with Padeem as your commander.
Powerstone Shard goes infinite and kills the table with Cogwork Assembler and 17 mana- which this deck seems like it could reliably generate.
Copy Powerstone with Cogwork (7 mana spent)
Copy Powerstone with Cogwork (14 mana spent)
Tap two Powerstones for 3, copy one with Cogwork (15 mana spent)
Tap two Powerstones for 8, copy one with Cogwork (15 mana spent, float 1)
Tap the last Powerstone for 5, copy it with Cogwork (16 mana spent)
Tap Powerstone for 6, copy it with Cogwork (17 mana spent)
Tap Powerstone for 7, copy it with Cogwork (17 mana spent)
Tap Powerstone for 8, copy it with Cogwork (17 mana spent, float 1)
You can keep doing this from here generating infinite mana until you decide to copy Cogwork with itself infinite times and attack with infinite 2/3s.
The reason I really like this combo is that all three pieces - Powerstone, Cogwork, and Mirror - can be tutored with Trophy Mage, Whir of Invention, and Inventors' Fair, which makes it very reliable. Also, not having Glint-Nest Crane in here seems like an oversight; it's a ridiculously efficient cantrip.