Even an 1/8" gap around a door will look too big, I would suggest either cutting the hole and using a different piece for the door that is more like 1/16" smaller on each side or using the 1/8" bit and adding some sort of trim that covers the gap and hides the hinges, if the door opens in it would be practically invisible, if it opens out I think you would have to either buy fancy hinges or see the hinge.