Heavy pellets do work in springers. Just look at this group! Also crown your barrels which is what I did.
Before crowning the groups were horrible, look below.
I was using CPL'S 25 yards
After corwning at 25 yards
left group(beeman kodiak match) right group(cpl's)
I don't like to use the beeman kodiaks too much because I don't want to weaken the spring, but I do like them for the long shots like 120 yards at cans.