Well, Josh, you got good suggestions for slicking up a pad.
But I'm gonna take this statement...
"I would appreciate your insight."
as an excuse to suggest something else. I suggest you leave that pad just as sticky as it is and learn to mount your gun so it doesn't matter. If you can do that, not only does the problem go away, but you will have improved your gun mount. I use Kick Eez and Decelerators on my target guns; I don't treat them because the pad never touches my body when mounting from a low gun hold. The first fundamental of a proper mount on a clay target is to move the lead hand first, meaning the butt instantly breaks contact with the vest.