Try this: When you want to remove worn paper, put the pad flat on a concrete floor and spin it with some pressure for about ten seconds. It will heat the adhesive, and the paper should peel off easily.
Different technique, same physical principle, same result: heat your paper disc with a heat gun (enough to melt the glue, not enough to set it on fire and melt your pad, too), catch the disc by its edge with a clamp (not to burn your fingers) and just pull the disc from the pad.
Get a second pad, and just change pads when you want to change grit. I always used that technique of heating, when the paper was worn and needed replacing. No intent to re-use it.