Perhaps we're speaking past each other. What I mean is, if you're using 12V motors, then make the H-Bridge supply 12V to match. If 6V motors, then make your H-Bridge supply 6V. When I say match, you have a bit of leeway because of losses in the Darlingtons, meaning if your're using 12V motors your bridge supply could be a bit higher, say 14-16V, without a problem. (If you were using MOSFETS, you would have less losses in the drive transistors.)
And all of this has nothing necessarily to do with you LM311 supply of 5V...
Yes I used an NPN. I just never used a open collector without a pull-up. When the NPN is on, the Darlington base gets a good logic low, when the NPN is off the darlington base sorta floats and momentarily oscillates. I would just add the pullups and pull downs for good measure.
But hey, I can't argue with success...