I know the rule but wonder if it would make sense to make the reroll after you finished rolling all your dice instead of at the beginning. Reason being that at the end is when the "damage or no damage" is done. That it would seem to be more "in favor"
Certainly anyway you wish to play it is great if it works for you. House rule versions are always a great way to mix it up. In general however, if rerolls are made at the end of a turn the game is dramatically slowed down as you are really taking two turns everytime there is favor. If you have fast rolling players it could work. I have found that rerolls at the beginning are great because you usually have a sense of whether the roll is good or bad and this allows you to maybe improve you position.