It sounds like you need to do a little bit of detective work to ascertain if the motor screws pinch the g'box and screw things up for you. Use two screws long enough to poke out the other side and use nuts instead of the motor and do everything up as if you were bolting the motor to the car and then test again to see how free the gears are by sticking your finger through the motor hole and feeling how easily the gear inside spins (perhaps it's a good idea to not have other gears in yet, and definitely detach the driveshafts).

My guess is you're pinching the bearings in the other gears when you're doing up the motor screws. This might mean the gear shafts are too short and the chassis halves press the cups against the bearings (or who knows what plastic distortion is at play in the chassis halves). If this is the case, short of trying another set of shafts (which may or may not solve the problem) I don't see other options apart form making your own shafts a tad longer or using some small washers/shims of appropriate diameter inside the chassis gear shaft locating cups.

What's "inchups"?