So..... how do I approach this? You've got about a dozen potential factors all colliding to (probably) generate your observations, and it is kind of a lot to explain. Let me try and hit you with the sparknotes.
If you don't shoot PBs, particularly higher power PBs, you might not be aware of why/how your form can affect your POI. In short how you place your ass behind the gun will affect your POI on groups. If you drop your shoulder under recoil or place your weight directly behind etc you can certainly walk your groups around. Some people deny this, but it is pretty trivial to demonstrate if you and your gun are good enough. Barrel length, muzzle brakes/moderators, gun weight, etc can all affect this equation.
I also agree that it shouldn’t affect accuracy unless it was having a baffle strike.
This though is completely untrue, in fact the complete opposite is true. Both firearm suppressor and airgun moderator design is a compromise between sound suppression and acceptable accuracy loss, among other factors. You can make a design which is very quiet and uses aggressive cross-jetting to accomplish it. You rarely see such designs though, because nobody is willing to tolerate the associated accuracy loss. Even in designs which don't generate cross-jetting like that, minor changes in how close the pellet travels to solid objects inside the moderator can open up groups without a physical baffle strike. It is a weird phenomenon to observe, but it is a thing. It is almost certainly more of a thing with airguns than firearms I should add, because airgun pellets are incredibly easy to destabilize. They have so little mass in their skirts (by design) but a great deal of surface area and it is right at the perimeter of the round.
As far as doing diagnostics to try and split what factors are causing what, you might want to start with just having someone else shoot the gun. Changing form and printing some good groups might be very informative. None of this BTW is meant as a shot at Donny.
This whole stacking tolerances thing of attaching moderators is a giant mess, and I'm more than a little surprised we don't hear about its consequences more often. Either way I hope something in there is helpful. If you have any other questions, I'll do my best to try and answer them.