It also strikes me that you may be moving your hand quite a distance to open the palm D, causing the sax to push to the right from the momentum of the movement.
Perhaps a key riser on your palm D would help with that, so that the key touch is close at hand and you aren't yanking the horn around to try and get to that key?
Perhaps a key riser on your palm D would help with that, so that the key touch is close at hand and you aren't yanking the horn around to try and get to that key?