First off, it's mandatory to listen to this song whenever you flip to Giant Wasp: Big Fig Wasp - King Gizzard and the Lizard Wizard
After looking over the cards and playing the pre-con, I didn't really feel inspired to play with Wasp. I also felt similarly about Justice as a whole. There just weren't any deck concepts that used the Justice aspect that compelled me to build them, and I didn't know what Wasp was supposed to be good at. So I did the natural thing and built a Justice Wasp deck.
G.I.R.L.
I decided to build a deck around the Alter-Ego ability that brings two cards with a mental resource back into your deck from the discard pile. It seemed like being able to get multiple uses out of key cards with mental resources is something other heroes couldn't do, and trying to build around Small But Mighty (tiny hero ability) seemed like a trap. Looking through the cards available in all aspects with a mental resource, two cards stood out: Lay Down the Law and Clear the Area. Using Justice will be helpful for a deck that looks to routinely flip back to Alter-Ego, and Lay Down the Law in particular will work well to clear threat from the main scheme that accumulated during the turn spent as Nadia. That being said, the absolute best cards to bring back when possible are Genius and probably Nick Fury. Using Nick 2-3 times for each pass through Wasp's deck can feel like cheating. I have been testing this deck in some fairly minion-heavy scenarios, so the 4 cards I generally bring back for each flip down (2 cards the turn you flip down + 2 cards the next turn you start as Nadia) are Genius, Nick Fury, Pinpoint Strike, and either Lay Down the Law or Clear the Area. Ironheart is also a good target along with Swarm Tactics if your deck is getting thin and Ant-Man ally is still in there.
Basic
Turns out the answer to not being excited by many Justice cards is to just not play them. That was a more difficult proposition prior to Wasp's pack, but now with The Power in All of Us, Ironheart, and the Miles Morales Spider-Man ally things are a little easier. Being able to generate double resources for powerful cards like Avengers Mansion, Helicarrier, Quincarrier, and the basic allies is very strong. I originally ran Heimdall over Down Time but it was one expensive Basic too many and I didn't want to spend more than one action recovering on the turns I flipped down to AE.
Justice
Clear the Area and Lay Down the Law are obvious includes based on the central thesis of the deck, but I also included #Quake because All Two Cost Allies Are Good(tm), Under Surveillance because it's a lot of value for a solo player like myself, and Stealth Strike and Skilled Investigator because they provide more value for defeating enemies and schemes to pair with Small But Mighty.
Results and Final Thoughts
This deck beat Expert Klaw with Anachronauts fairly easily, but has struggled against Expert Mutagen Formula with Doomsday Chair. All games against the latter have been very close, but this deck doesn't have an answer to multiple minions with Guard. Nor does it have much healing beyond the Recover action and the last stage of Mutagen can easily go from 0 threat to completed when you're unable to clear the 4+ minions on your board. Otherwise, I would say it's the most interesting Justice deck I've played to-date in terms of learning how to pilot it. Generally, I think about staying in hero form as long as possible and flipping back to AE when the damage gets too high. For this deck, you have to rewire your brain to think about flipping back to AE whenever threat is low enough in order to avoid extra attacks. This deck gets rid of threat far more efficiently than damage, so you have to think of threat on the main scheme as a resource to spend like you'd normally think about HP. Beyond that consideration, if you can get at least one or two resource/card generators early such that you can play two of attack event/thwart event/ally every turn, then you will be in good shape.