Sounds like broke scope syndrome. Do you have another to check against? If you do, when trying it out - DO NOT ADJUST windage and elevation on the "try scope". All you are doing is to verify grouping of the rifle, NOT zero. It doesn't matter if is a foot off aim point. just look for group.
You checked the stock screws. Is barrel pivot screw pretty snug also?
Wide variations in pellet velocity will spread out groups. Do you have any chronograph data?
On most of my springers, a new breach seal sits about 0.010"-0.015" above the mating surface. Does the breach seal look good and does it pass the tissue test?
I'm assuming this is the rifle with the factory new NP2 piston assembly? I've had new piston seals that needed a few dozen shots to wear-in .
There is always a little fresh-rebuild-dieseling also. I use a thin coat of moly paste lube in the high pressure area, but also know the moly carrier will diesel for the first 3-5 shots. My chronograph data shows that there can be a 50-100 shot gradual change which I think is the new piston seal wearing-in.
(edit) Have experienced velocity variations (flyers) and a change of average velocity (up to 30fps) until seal is bedded and everything stabilizes. Large groups normally tighten up really well after this wear-in stage.