Barrel Vibration / Harmonics
When you look at a barrel on an airgun it seems like a pretty sturdy chunk of steel, but if you look at some high speed video's of airguns being fired (I had a link to one on YouTube a while back, but I don't know what to search for now). You'll be quite shocked to see just how much vibration takes place on a barrel as you shoot the gun.
I suppose when you consider that you're forcing a lump of lead through the barrel at over 500mph, it's reasonable to assume that it's going to vibrate a bit.
I'm not entirely convinced about tuning barrel harmonics - I guess it might work.. I dunno?
One of the reasons why when measuring scope height for ballistics calculators you shouldn't take the physical measurement from centre of scope to centre of barrel is that you don't know where the end of the barrel is going to be when the shot is actually taken (because it vibrates).
That's why the tin foil method of measuring line of sight height is a more accurate measurement, because it also takes account of barrel harmonics too.
So... given all that, I'd say that it's quite possible that changing to a different pellet, could change how the barrel vibrates and that could mean that a different pellet could make the gun feel more 'flippy' and it also could explain why your POI might change for windage and elevation, it doesn't necessarily mean the BC is different though.
What you all need is gun with a really thick and sturdy barrel with an underlever to help hold it all in place