The size of the pad will determine your length of pull. It likely will have little effect on recoil dampening. You may want to fool around with the shim kit and reduce the drop at heel. Sometimes that will improve the push of the recoil into the shoulder and away from the face. Messing with stock dimensions can change your point of impact, so be prepared to spend time patterning your gun after changes to see where the point of impact is.
Realistically, your inertia semi auto 12 gauge only weighs about 6 3/4 pounds and will always kick due to its light weight. (Shotguns used primarily for shooting competitions typically weigh 8+ pounds) The easiest way to reduce recoil is to reduce the payload of your shotshells. 1 1/8 ounce loads can be swapped out to 1 ounce. For clay shooting, you'll not likely notice any difference in performance. Your other alternative to reduce recoil is to add weight to the gun; talk to a gunsmith or shoot coach to see where the gun may reasonably accept added weight.