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On the mounts, I have never seen nor would I trust thumb screw bases. I use SportsMatch bases for all my 11mm Dovetail mounts. They are steel and amazingly solid using 2 screws per base, 4 per ring-to-scope. I use steel Warne rings for any Weaver rails. Never overtighten rings to the scope. I use the short handle of the wrench not the long handle. Rings over-torqued will possibly warp a tube. Tighten base screws first then tighten the top side screws opposite the base side screws going in an X pattern. Like that when you tighten lug nuts when changing a tire. I do all this after I have lined up the crosshairs with a plumb-bob 10 yards out to make sure scope isnt cannted/tilting to one side.
You may be shooting pellets the H95 hates. Use soft lead JSB brand first, round nose dome diablo skirt and see how that does. Rest the springer on your hand on a bag on a steady, firm bench or table.
Dont get over worked and try to force the rifle to do perfect, just let it show you what pellets work best. Clean the barrel gently, check for burrs in breech. Is the rifle barrel locking well or is there play? Break barrels change the relationship between the scope and muzzle everytime (in theory) you cock it. Under or side levers obviously dont.
PCP's are just more accurate by design as the moving parts are just a hammerspring, shear, trigger and other small parts. Springers have actual pistons and valves and much larger springs that shift and jolt before the pellet has left the barrel. Good luck!