I have played a similar variant here on chess.com using a forum discussion.. no time limit for move since time is not really relevant anymore (and that's the main reason it can't be really called bughouse). The moving mechanism was also slightly different to simplify things: player A started moving with white, then player B moved on both, then player A moved on both and so on. Since a player was moving on both boards at the same time he could capture a piece on one of the 2 boards and drop it on the other in the same move.
Correspondence Bughouse.
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I'm very interested in bughouse theory and I think it would be interesting to play correspondence bughouse. Could chess.com add bughouse to the daily chess mode? (Obviously one player should be able to play both sides.)
(Stalling): To avoid stalling I think it would also be a good idea to force player to play their first move and all their consecutive moves at the same time.
The only way you could reasonably do this is if you were to give both players the same amount of time to make their first move but instead of showing the actual move that has been played you just show "Your opponent has moved" and you have some amount of time to finish your move.
(white white, black black, white white, black black, etc)
I don't know, I feel like this could be really interesting.