Thanks, Joe.
It is best to explain a POI change to aiming error or trigger control error. Those are the 2 fundamental tasks. So it seems that your problem solving approach is ideal.
When grouping, I always pull the trigger slowly enough, only when the sight is on the desired POA, adding about a tenth of a pound at a time, to allow me to see the sight at all times before, during, and after the trigger break.
Even so, my rounds seem to go to a different place when using a muzzle rest. It may be a lens interaction issue if I'm not actually seated, but rather leaning down to the rest. I usually wear prescription glasses. However, I was trying to deduce whether it was somehow effecting the POI by placing the dust cover on the rest. It seems unlikely, given that the barrel is locked up with the slide. That being said, it is also locked to the frame by the slide stop.
I will give it another try this evening to see if using a wrist rest eliminates variables for me.