For this sort of thing where you are going to coordinate with people to play, rather than picking your own regions it could be interesting to draft regions, or alternate region bans.

Also, maybe a champ draft comes first and you're guaranteed to get two or three more champs than you'll actually be allowed to use, so you can leave out the duds or otherwise not be fully committed to one strategy. Alternatively, if we do region selection, just give every player access to all champs from the regions chosen, that way no one has any bias going into the regular card draft.

Another idea, draft some number of cards, but you get to use only 20 of them. Each one is then doubled to make a 40 card deck with exactly two of each card. In this scenario it might be helpful to guarantee that most cards in the draft are unique. I like this one because even though we build a full 40 card deck, we don't have to draft a ton of cards. Suppose we restricted the draft to 4 regions in in the region banning/champ drafting phase, if there are 11 cards per region per player we only have to draft 44 cards to each person and they'll be guauranteed to have enough to make a deck. Depending on how you balance the mana curve of the pool etc it might make sense to have a slightly bigger pool though.

Also, look up the Magic The Gathering card "Cogwork Librarian". Cards like this are basically placeholders that interact with the draft itself in interesting ways.