Is the V of the Caldwell bag somewhat grippy? More so than your open palm? Reason I'm asking is my best springer shooting was either with the balance point of the stock resting on my wrist or on a paint roller rest like this:
Groups seemed to degrade if the rest was something that the stock grips onto.
I have to say the challenge of shooting a springer accurately is enjoyable in a conquest sort of way. Everything has to be just right to get those ragged hole groups at 25 - 30 yards. That's why I use springers for practicing shooting form and reach for a PCP when I need to make a confident, humane shot on a pest. No warm ups and no retries.