After I made the above post I got to thinking about it. I always mount traditional muzzleloaders more to the outside of my shoulder in the pocket between the bicep and shoulder. Especially, with curved butt plates. That's to the outside of the PAST pad. I got to thinking what would happen if I shouldered the gun like a modern CF/shotgun further in on the shoulder.
So, I put on the pad, and started to shoulder it in the new position. It felt strange at first, but I adjusted fast. The butt plate just stays on the pad, but it's on it solid. I'll have to get used to this, but it's going to make the hunting loads a lot more comfortable. As an added benefit the LOP was always a bit short for me, and now it's perfect with the pad thickness.
Thanks for bringing it up. I had given up on the pad, and I never would have tried it again.