jwatte:
The arrangement you suggest is exactly the same arrangement that the body diodes is providing, right? Your suggestion is that the body diodes are poor performance as flyback diodes, and I should double them up with something better?
Can I use some 1N4001s? Do I need a high-voltage Schottky? Something else?
Yes, same arrangement - across the FETs.
You don't need "high voltage" PIV, >= 1.5 * V_supply ought to do it, because they're normally back-biased. When they conduct, it's all about forward current. Schottky is best , but a decent rectifier is better than the "body diode" (which is a zener equiv, after all.)
The cap network on the motor is for noise reduction which I doubt is your issue.
Like I posted last, the very best way I can think of to preserve your USBtinyISP (et al.):
Disconnect motor voltage before and during re-programming (or anytime that the USBtinyISP is connected.)