Why isn't this a thing? I looked around for a bit, but it seems that most people either play four-player bughouse or crazyhouse. Why not play bughouse with two players and one clock? Just allow a move to be a normal move or drop on either board, and introduce the concept of a conditional pass, where player A passes but player B then has to make his next move (which cannot be a pass) on the board of player A's choosing. Seems like this would solve both of bughouse's problems: stalling, and the need to find a suitable partner. Yes, you could just play crazyhouse, but bughouse is fun too.
I suppose you'd also have to make it a rule that player B's first move on his white board must not be the same as player A's.