H-Bridge simple performance
Without the pullup/pulldown resistors even the tiniest transient condition on startup may cause shoot-through and fry the bridge. I would not omit those.
Looking at the datasheet of the TC4428ACOA, I think you may be able to remove the gate drive series resistors. I don't see any limit on the drive that will be exceeded if you do. However they may be there to damp ringing, so you should check that with a scope if you're going to take them out.