I think a great solution would be simply whoever takes a king first, it would solve many of these complications. (teams only, mate is better for free for all)
teams variant

but i think i prefer to checkmate. i'd like to preserve that a check is forcing, and you must defend. you cant escape by capturing another king or whatever.

Capturing the king to win should indeed be possible in team mode. I have not seen it happen, but should be possible.

tried to make a teams example. note that if blue play QxN on move five, he still gets mated

i agree king capture should end the game. probable does.
not sure if i like allowing non-defense of a check.
btw i've wondered what if your partner could always still intervene, even after what is now checkmate.
it's kinda not ok that green can get mated on a square that is covered by his partner blue.
i think i'm suggesting turning the game into regular chess. black vs white.
would drastically reduce the amount of mating combinations.