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Hi, Jaan:  I made a Chess for Three game on a triangular board (in the
alphabetical index here) some years ago and had to deal with the same
issues, of course, especially what to do with a dead King's remaining
men.  I've found that the two weaker players tend to gang up on the
strongest anyhow, as a matter of survival, until one King falls, at which
point, in my game, his pieces become inert and may be taken by either
player as required to get them out of the way. My thinking was that for
the capturer to be able to recruit the captured King's pieces would
constitute an overpowering advantage which would preclude further fair
play, although a subsequent victory by the (now) weaker player would be a
very satisfying 'David vs. Goliath' feat.  So how often does the
disadvantaged guy win in your game?
 The shape of the board may affect the practicality of a rule requiring
mutual assistance; on a triangular board a moment sometimes occurs when a
Queen has both of the opposing Kings lined up in such a way that she can
take them in sequence, taking one and 'checkmating' the other. I think
that would be less likely on a board with square cells because it's
easier for a targeted King to duck to one side.