Hmm, I think I understand what you are saying. Basically, whenever I want to utilize the other two FET's, make sure I leave suitable time between turning two of them off, allow all current to leave the circuit, before turning the other 2 on? I don't think we're going to be doing running the motors using PWM so the only chance that 'shoot through' will occur is when changing directions, I presume.
In that case you might get away with it because the average power dissipated will be low - be aware though that the high-current spikes will potentially cause odd problems. You can easily boost the gate drive current with a pair of transistors as emitter followers BTW - see this application note http://www.diodes.com/_files/design_note_pdfs/zetex/dn80.pdf