Just wanted to follow up with an update. I have attached my most recent 5 shot group at 30 yards. Obviously not all that impressive, but much much improved compared to the 8 inch groups I was getting before. Thanks for all of the tips/advice everyone shared.
If you are new at springers, 30 yards is quite a ways. It was a while before I trusted myself to snuff a squirrel at that range. I started out at 15 or 20 yards to sort out what pellet I should be shooting--and yes, I had some that did 4 inch groups at 20 yards! Be sure to test plenty of pellets, starting with the ones people giving reviews say it likes.