And, for 3rd party characters, I think the only ones with a chance to get in are Mega Man and Bomberman; any other one seems impossible to me.
Nothing is impossible. Nobody is impossible. As long as they meet the requirements, they're not impossible to join the brawl. True, some might have a lower chance than others but it's still not perfectly impossible.
The only impossibles are anime/manga characters, characters who have not originated from video games and characters who have not appeared on a Nintendo platform.
I'd say maybe Shigeru Miyamoto is impossible because he has originated in real life? I don't know though, correct me if I'm wrong.