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But I wonder if you consider a position p, and then consider all possible one-move prior positions, p', the "correct" p' is the one for which p offers the greatest expected gain according to minimax? Kind of a greedy, local implementation of (roughly) the idea you posted.
This isn't quite a game, yet - and I instinctively feel there should be a natural, maxi-min, co-operative game possible here.
On further thought, the reverse sequence would not be guaranteed to be the optimal way to get to the original position. Without being too precise, let us assume any "reverse move" leading to p' which can lead to p is legal. Then here is a counterexample:https://lichess.org/study/KieA8vh1
I guess similar motifs can be used to make the optimal solution arbitrarily better (?), but the idea of a chess variant having some neat reverse play property is very interesting. Maybe the right way is to think of maximin / and objective functions instead of just chess variants
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