That would help with the greatsword and maul, but none of the other two-handed weapons. And I find rolling d4s annoying (the whole picking them up thing

).
That was why I added the third option about raising a low roll to half the die maximum. No rerolling necessary. Using a base 3 is too low, however.
I was actually thinking about going the other direction for a simpler GWF as well. Since you are using two-hands, you are more accurate with your strikes. I didn't include it in the OP since I was trying to keep the "better damage" concept.