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I would propose one more rule: Checkmate does not end the game. A player who is checkmated must immediately remove his/her king from the board and end his/her turn.

Another way you could make it (that I might have thought before, and might have seen it before also but I forgot), is to make the promoted pawn to be able to move and capture anywhere, so the opponent is in check and the only way for them to be out of check is capturing the promoted pawn, and if they can't then it is checkmate.

Here is that Capablanca - Alekhine game, and if you click on the link 'Click here for Sorokhtin's original file in ChessBase format' on this page, you can see an extensive analysis of that game meant as correction to Kasparov's analysis in one of his My Great Predecessors volumes.

Capablanca - Alekhine, [1927 World Chess Championship Match, game 11] ended with two White queens and two Black queens on the board. Many chess players prefer keeping the option of multiple queens.

Here's an example of two 'immature' players who played a chess game featuring multiple queens.