I don't know if this depends on different platforms, you will be told "you shouldn't be messing your save files like that" if you only delete both persistent files and load before making the decision, maybe they are other factors connected to this unchangeable choice.
(P.S. playing on PC)
I see. I just replace persistent file (one before choose a choice for Nameless) to current persistent file in both folder and it work normally. I think if you just delete it and not replace it with a previous one, the game will show a dialogue like that. BTW I play this game on PC too.
Warning: This kind of action may cause some bug for your game. Please consider it with care.