Good morning
@ThomasT I think I understand what you are saying. But if you are making crosshair adjustments with your right hand, when you squeeze the trigger there is a very good chance that the trigger pull alone will exert a different force on the trigger and move your cross hairs.
Using your new rest and just for giggles, align your cross hairs with no body part touching the rifle, just use the front rest elevation and windage adjustments. Then try 2 different trigger techniques:
1st pinch the trigger between your thumb and index finger to break the shot.
2nd method is to place only the tip or front pad of your index finger and pull starlight back with no other part of your hand touching the rifle.
Let me know the results of each experiment. In both experiments exert force on the trigger, but don't break the shot while watching the crosshairs while you relax the force and repeat it. Did the cross hairs move? Neither may work better than your method but its worth trying. Some rifles just need to be touched in different ways and these are just two different ways to try. I am not sure why because it may just be a harmonics kind of thang?