I've never played Multi-Man, but one thought is to let the booted player continue to play and use their units to have a board presence. This may also help situations where one player is winning by a mile.
I agree. That's also what I'm suggesting in the OP. The monster can be eliminated from the game. But the player can stil control/spawn units and try his best to snatch a kill or two before the game ends.
It's not going to be super interesting,but it's way better than sitting stil, and it will make the endgame go by much quicker, since the odd's of a monster taking damage each turn increases because of repeated attacks from the "monsterless" players units