Because a springer needs to be removed from the rest to reload, make sure you return the gun to the same position on the rest. Placing the rifle on the rest at different places along the forearm will produce radical shifts in POI. Springers generally do best when rested on something soft like a sand bag or rolled up towel about 1-2" inches in front of the trigger guard. Find a good dome pellet like RWS Super Domes or JSB .452's. Pull a doubled-up length of 30-50# test monofilament line with a patch dampened with a few drops of Goo-Gone citrus cleaner then a few dry patches to eliminate a fouled barrel(common) as the problem.
We'll watch the forum for your results.