Thriller Fan, if one side has two kings, you should be able to take a king then if possible, only having to checkmate the one left standing. After all, the whole idea of checkmate rather than taking the king was that it represented a position of inevitability. If only one king is mated though, things aren't so inevitable since one of them is disposable.
Also, to verybadbishop, although the bishop is pinned, surely it would be happy to capture the white king, as it is a king after all.
I have a friend that would play "ninja chess," wherein all rules of chess were the same, except that each player would write a small "N" on the bottom of one of their pawns.
In addition to it's normal movement, that pawn can move and capture as a Knight, but cannot promote. Neither player knows where the other player's "ninja" pawn is, until it moves likes a Knight.
I thought it was stupid, but he liked the idea.