It would be nice to add an extra option to the autosave feature – saving at the beginning of a turn. This way, you wouldn't have to ask your opponent to save at the beginning of their turn.
I didn't quite understand your point; could you explain it? Saves at the beginning of a turn are not different from saves at the end of a turn, if you use them to analyze your opponent's move.
However, you will still have to ask for your opponent's saves to check how they played.