If you don't mind me saying, this is one hell of a mutator !!
However, it is probably difficult to keep track of everything going on at once, I would suggest three modifications, which may be combined or taken independently. My personal choice would be to use the first two, and discard the third.
1. Keeping pawns out of the sequence until they promote.
2. ONLY piece which more attacked than they are protected promote. That is, after 1. e4 e5 2. Nf3 Nc6 , the pawn on e5 doesn't promote because it is attacked once and defended once. The King could count here.
3. Limiting promotion to one piece at a time, no matter how many pieces left unguarded.
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((I believe there is a mistake in the example game... in white's fourth move promotion details, if you would check it out.))
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I nominate this game to be in the next Game Courier tournament (using modifications 1 and 2 above.)