That's a pretty big extension. I'm going to see if I can make something that slides up and locks into the back of the stock. It'll cover the entire area of the butt and lock in with set screws. If it works and looks good I'll also use it as a base for making an adjustable stock system with pad.3 inches would be good.
Maybe a 2pc 3D printed part that attaches to the picatinny and sling slot?