By the time this thread makes the circuit you'll become aware of every problem that everyone has experienced. This is a good thing. By then you may have come up with a unique one that will help some one else.
Here's two suggestions:
1) Don't load the gun. Set up on the target. The gun should be in "the" natural position (there's a correct name for it but it slips me at the moment). That is, no muscle pressure should be necessary for the cross hairs to be on the point of aim. Brake the trigger. The point of aim should not have moved.
2) Takes too people. People one in secret (from people two, you) either loads or does not load the rifle and safely places it on the rest and rear bag. Then you do suggestion 1).
Don't video these sessions. Be prepared for a little self inflected humor.
Been there and done that. No one ever speaks of those sessions.;)