Gunnut has a good point about the side to side movement or rotation when you loosen/tighten the screws. Thinking about it, one of the Remington stocks that I had was not only higher between the action screws (so that the stock bowed when tightened down) but it also twisted to the left when loosened. It got trashed.
I think that the cold bore, dry bore, clean/dirty bore is the place to start. I know that the Handirifle that I had with Microgroove rifling would shoot 8-10 high and to the right with the first clean, dry bore shots. After 2-3 fouling shots it was ok.