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Just a follow-up, something I thought of: perhaps you should not be able to
check your own pieces with your opponent's move. That seems to give a huge
advantage to Black: as Black will play White's move first, White on
Black's move will frequently have few options as he has to move the Black
piece out of check. This is maybe less of a problem in the variant where a
player 'steals' his opponent's move instead of the players switching
for a turn, as if a player gives check to his own pieces, he will be the
one who has to spend a turn getting out of it. 

I like my idea but I am realizing how difficult it is to write about!! :)
Oh, and I'm registered now as well.