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Maybe your problem is that the rest you are using is too hard. Spring air guns have a lot of vibrations that can shake the barrel while the pellet is still in the bore if the gun is rested on a hard surface.
I'm no expert, since I just started shooting a second-hand RWS 48. But I have read and was told by the RWS tech on the phone to use the softest rest possible. The RWS tech says he uses a pile of quilts, sets the rifle on the pile so that it points exactly at the bullseye without him holding it, then gently slides into place and holds the gun very lightly.
I have been shooting from a bench, using an adjustable bench rest cradle with a sandbag. The RWS tech thought the sandbag was about as hard as I might be able to get away with, and I am thinking about making some other sort of soft supporting surface for the cradle.
What I have been doing is balancing the rifle on the sand bag and positioning it with the cross-hairs centered on the bullseye, then gently gripping it and firing the shot. (If I held my .270 that way, it would demolish my shoulder.)
I have been able to consistently make single-hole groups that are about 2 pellet widths at 50' (17 yards) using the Diablo Exact and Kodiak pellets, but no so good with Crow Magnums, Super Domes, or several flat-nosed "target" types. Beyond about 50' my groups expand more than proportionally with the range increase. I am still not sure that my barrel is not fouled, so I may be able to get better groups from other pellets as I pursue my refurbishment program for this second-hand gun.
If you have already tightened the stock screws and scope mount screws without improving your groups, then I think you need to get some better pellets and work on your grip. Also, possibly move your target in to 50' or less. As you found already, you can't sight-in until you an make a good tight group.
SL1
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