Tenet Inversion Chess

In the universe of Christopher Nolan's recent movie Tenet, it's possible for objects and people to be inverted so that they move backwards through time.

It would be fun to create a variation of Chess that's inspired by the time-inversion physics of the movie.

Here's what I'm thinking:

Starting position is the same as standard chess except, all pawns are removed from the board and set aside.

All pawns are inverted in time. Meaning, they can be uncaptured and their only legal move is backwards on the board, except when on row 4 they can move backwards either one or two squares to row 2.

Un-capture is possible when an enemy piece is sitting on a square that could legally have held a pawn. Uncapture is executed by moving the enemy piece back to valid prior square and then "materializing" a pawn in the square where the enemy piece was just sitting in the near future (as described by a time-forwards observer).

Any time a pawn is moved (including at the uncapture move), it is experiencing time in reverse, and so it also has the effect of undoing the last normal move and also rewinding the clock to where it was at the start of the previous turn.

At every turn, players can choose to use their other pieces to make normal moves which propagate forward in time, like normal chess, or inverted pawn moves which are essentially a forced rewrite of history one move at a time.