A few things:
How does this work if you have a comp where a lvl 2 is the earliest you can get (like Demon or Glacial) and one of them isn't available in the carousal? Do you just pick that 1 person and roll with them until you get a Demon or Glacial?
How you handle things like Imperial where they have a lvl 1 unit (Darius) but your next unit to complete the 2/2 buff isn't until Kat at lvl 3!!!
Further to that, Phantom would be awful. Sure, you get a Morde early, but you can't get the 2/2 buff until Kindred at lvl 4 (ouch)
I personally think Noble, Wild, and ESPECIALLY Knight are super abusable. Those 3 can all be completed by getting only lvl 1 characters, but Knight can do 2/2 with three lvl 1 options.
Are you allowed to pick anything in the carousal or do you have to pick based on your assigned comp? (I.e., can I pick something not from my comp, but they could have been from someone else's comp, for the item and then sell them.)
In my humble opinion, you should only be forced to go into a starting class that can get you to the requirement using only 1 and 2 lvl champs. but need both?
Brawler (WW + Rek/Blitz)
Ranger (Vayne + Varus)
Sorc (Kass + Lulu + Ahri)
Assassin (Kha + Pyke + Zed)
Void (Kha + Kass + Rek)
seem like they would work. I think you could add Demon and Glacial as well if you allowed people to at the very least fill out your roster with randoms so you were maxed to 3/3 champs on the field. Just don't allow people to make those champs 2 star. If you pick a random to fill out the max, you cannot upgrade it? Then when you got a Glacial or Demon (both start at lvl 2s) then you sell your randoms 1:1
That gives you 7 comps. I'm not sure what the 8th could be to round it out. Maybe Yordle since Trist + Lulu + a frontline character to fill out the 3/3 is somewhat viable until the lvl 3 champs become options.
I could be totally off here, but I think if you get Knight, you have an extremely good chance of completing it within the first two PVEs and then you can do whatever while others suffer. Wild and Noble somewhat similar.
You and I should play and pretend we've got a few of these and see how it feels.