Major poi shift with just ammo

So I am in process of sorting out and tuning a springer. Been working out which ammo to tune for as a primary choice. All 3 daisy hp(oldversion), rws super hp, and Norma ft 15.9 will group reasnably well and center on the bullseye. Both excite hammers, and h&n ftt domed ammo will shift to the right where I don't have enough adjustment to bring them on center.. .of all 5 the h&n groups the best, but is over an inch right of center at 10 yards. Ir would be my preferred choice if I could get it in the center. So far the only way to do that has been by mounting a scope with more windage adjustment than either the std. Dovetail or peep sight. The scope makes this rifle much heavier than I want to carry around. Any thoughts on this? If it was all ammo I would assume there was a sight mounting issue with the alignment front to back. This rifle hates nothing more than cphp...which is irrelevant here, but it throws horrible groups at close range.
 
The finickiness of airguns toward pellets has always surprised me at how dramatically POI can change. Springers & PCP's alike. I think that's why I like my Original Smooth Twist barrel guns so much. Designed around a certain pellet & for the most part, only shoots that particular pellet well. I'm OK with that. As long as I get ACCURACY.
 
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The finickiness of airguns toward pellets has always surprised me at how dramatically POI can change. Springers & PCP's alike. I think that's why I like my Original Smooth Twist barrel guns so much. Designed around a certain pellet & for the most part, only shoots that particular pellet well. I'm OK with that. As long as I get ACCURACY.
This idea that 1 pellet delivers the best groups as long as you don't want them on target is driving me a little nuts...
 
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maxed out and still off center by an inch plus at 10yards.
 
I would try cleaning the barrel, polish the crown, bore and chamber, start small and work up. The recoil difference from pellets can do that too, one I have will shoot to the right if not held right. It could be burrs, bent barrel or uncentered bore.
Crown is polished, barrel was cleaned may 100 shots ago. Bore has been very lightly polished but could potentially benefit from a little more. Rifle has been detuned slightly atm in prep for upcoming work. Right hand shift was present before and after any work, not caused by it. Chamber, and transfer port are untouched other than some deburring of the cocking arm slot etc.