Is it possible teh rubber mounts allow the engiine to twist when powered up? If so this can change the orientation of the prop to the hull while under power. If the prop is parallel with the transom at low rpm's, then when powered the prop walks a bit causing the undesirable condition.

Try this. Keep the boat stationary, get on one side of the boat. Power the motor up and keep an eye on the prop. Notice if it moves in orientation.