You can't. You have to share the best move ahead of each move.

Waiting for a specific duraion may yield different results depending on CPU usage or other variables.

Players only reference the engine to resolve a claim, after the move has been played.

Ah. So part of the fun is not knowing which move is forbidden, ahead of time.

Yes. You also have to be good enough to be able to guess what is most likely to best the best engine move.

No, there are no top engine moves in practice, and in theory.

Only in the general case, for simple (mostly endgame) positions it is quite possible to exhaustively search the move tree and find the absolute best move. Those can be found by current engines and future engine development won't change them anymore. Such a move would therefore always be the top engine move.