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compromising looks similar to ambigous, but closer to chess.
I am more seduced by one-and-half, maybe we could add that black start with +0.5 for compensation. What do you think? And of course if it is implemented, it must be implemented as a fully playable version with move sequences (as we have move sequences for backgammon, too)
mangue: Move-and-a-Half Chess sounds very promising to me. I'd love to playtest it first, to see whether the bonus values that I mentioned give a good balance between White and Black wins. If it generates good complex play and yields about 50/50 results, I could see asking for it to be supported here. It reminds me of Three Checks Chess, with its wonderful imbalances between force+development vs. the number of checks delivered. Plus it could have some great mating threats and sequences like those seen in Progressive Chess.
wetware: I agree that Compromise Chess is a should-be-here variant, but there are at least two possible checkmate rules and II am not sure which one is better. Although your ruleset makes perfect sense, the take-the-king variant also does, that is, if you have only one way to get out of check, you have lost the game. When you are not in check and have only one legal move, it should probably be counted as stalemate.
Move-and-a-half chess is an interesting idea, that I didn't hear about before. Probably only play-testing can tell whether games will not always be n times a single move, followed by a big series which leads to checkmate.
mangue : Yes, I would love to see multi-move variants here. They are well suited for turn-based play because the games are usually short. Marseillais is good, but my personal preference goes to Double-Move Chess (the take-the-king equivalent).
nabla: For Compromise Chess, I had never heard of your "forced move ends the game" rule option, until you mentioned it. I would still prefer the "forced moves must be played without compromise" option, for two reasons: (1) it was what the game's inventor specified, and (2) my admitted personal bias in favor of endgames, and the way endgame theory changes in specific variants. I'm afraid that in the "forced move ends the game" version of Compromise, very few endgames would ever be reached--we would virtually lose an entire phase of the game, for no good reason that I am able to see.
wetware: As for (1), what I read in the Encyclopedia of Chess Variants is that Fred Galvin issued two games in 1958, Refusal Chess and Compromise Chess. Compromise Chess is played with the rules you stated, and Refusal Chess is designed as the over-the-board version, where you have to play one of your two moves over the board, and the opponent can reject it if he wants. It is virtually the same game, but for a reason I don't know in Refusal Chess Galvin decided for the take-the-king version.
Now, I am not saying that one rule is better than the other. I generally prefer take-the-king rules, but in this case it is not a real take-the-king rule, because if it was, the mated opponent could refuse the move which takes the king, so a double check would be needed to win the game (duh!). Regarding endgames, I don't think that it should not make a big difference (but I share your bias!)
mangue : Where did you read that ? That must be a typo :-)
nabla: It looks to me as though nothing short of K+Q vs K would be sufficient to force mate in the Compromise variant; K+N+B, K+B+B, even K+R (surprisingly?) can't get the job done.
K+P vs K endings are different, too. The "winning" side needs to have at least 2 pawns (and those must be on different files) to force a win.
Sorry to get so deep into the weeds here, but I find this stuff fascinating. :)