Nobody said Hellboy?

He met Batman both in comics and in video games.

Oh, man, yeah. Batman/Hellboy/Starman. That could make for an interesting team-up, especially if Batman and Starman can use their team abilities to make up for Hellboy's weaknesses.

as a Judge, i would welcome your idea of "Batman and peeps he's crossed over with" as a better team than "Uni-Mind and Batman". At my venue, i'd likely give you a Theme Team for the effort!

This would be my immediate go-to.

EDIT: I also like the idea of Batman/Robin teaming up with Cap/Bucky, as that was an amusing story with the rivalry of "better sidekick".