I think a good solution can be: 6 - modifier = d6 to rerroll...
So, in the example above, you have a +3 modifier for the roll, but you roll a natural 1... then you could try to re-roll it, 6-3=3, so you will need to roll 3+ in order to rerroll...
Perhaps this second roll could be without modifiers...
Now I need to think of the possibilities to re-roll the money.... that's because a player in our league allways rolls 1!!!


Anyway, what do you think of this possibility to re-roll the FF?!