Ok, maybe another daft idea and I really do not know if it has any merit, but:
Having recently experienced the effect of slightly loose forend stock bolts on a springer I have begun to ponder if anyone has ever tried a form of 'dampa mount' for stock bolts?
Custom seems to be to have stock bolts tight i.e. clamping woodwork tightly against the action. Any resonance / movement from the 'recoil cycle' is immediately passed to the stock and hence to the shooter's grip (yes I do know about a consistent, relaxed hold for springers but even so there is an influence from the grip, as witnessed by poi changes with grip position).
So what would be the effect of having some form of dampa-mount to mount the action to the stock? Could this be done by e.g. sandwiching a rubber buffer between two screw cups? Would the rifle become less hold sensitive? Is this what Gamo are doing? I do not know because I have not seen their recoil reduction system, but have seen and shot dampa-mounts for scopes and the BSA dampa-mount system on early Mercury rifles.
I am aware of 'bedding' stocks in the action but think this is different.
Does the Gamo system work? Does it produce a less hold sensitive rifle?
Just daft thoughts...

Cheers, Phil