Yup and I tend to store my break barrels “broken” so as not to compress breech seal. I leave my TX “broken” too.
Frank is correct. Your groups have nothing to do with the bumper. Your problem may have to do with a leak at the breech seal, though. You can try the tissue test to see if you have leakage there. I store my TX 200 with the cocking lever in the unlatched mode. When latched there is constant pressure on the breech seal, compressing it. Over time it takes a set in the compressed position and does not seal well. Note, the breech seal consists of two O rings.
While an older thread .... FYI on the cocking handle being left unlatched when stored IMO it does NOTHING simply because the main spring has the piston bottomed out and is pushing the Comp chamber forward against the seal already.That alone will crush the breech seal and flatten it over time.JMO on this ...Scott