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: As I read on chessvariants.com, you are a fellow organiser of marseillais chess... but well, I get bughouse is more sexy this millenium

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: http://pages.citebite.com/t1i7g2w6k1yys

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. :)