This is one where a bit of pre-game management could be useful.
You know there is an aspect of the game you aren't going to follow to the letter of the law (foul throws). So at the start when you say hi to both managers. Mention it. You'll probably find 99% of managers will be up for allowing the retake of a throw. If they are against it, explain to them that you will be doing it anyway but will be consistent and fair to both sides.
The problem is when they have some skin in the game (once they see the opposition do a foul throw). They'll do absolutely anything to undermine you, at that point logic and reason doesn't matter, it is already too late.
I do this in my OA games, if the centre circle is ruined by mud or some of the pitch is crap (surface water etc). I explain to gaffer and captains at the start that if a part of the pitch is terrible I will allow them to laterally moves the ball out of it for set pieces, but to ask me first. Just anticipating the inevitable moment when a player sees the opposition move the ball out of a bog and starts screaming about it, only to have the player rocket it top bag straight after. No coming back from that.