I have one of the slip on leather pads also, but, on some of my short guns, it has a squirmy feel that I don't care for. It doesn't fit tightly on all my guns.
Then you have the wrong size pad..........
if it moves at all.......Both of mine fit extremely tight on the 25+ guns of different makes that I have used them on.......very firm indeed, but I only bought two of the
small size ones as I had been told the other sizes were way too big indeed......and all my guns have uncut original factory wood ........and I am tall as well.......small is the only size that fits firmly IMO..........