When I was doing ADA, we used cores to roll the liner off of new and old plex. If you can get 6" of the liner loose, tape it to the core and roll it off. The hard part is getting it started. Once you do the even tension across the liner keeps it from tearing into small pieces. Keep the core and use it until it gets too heavy. The adhesive from the previous liner will stick to the next one.
If your doing smaller pieces use a dowel or something round. We found starting from a corner and working diagonal works better on smaller pieces (18" x 24 or smaller).
We back painted a lot of plex and started using this method to keep the plex clean and free from hand prints.
Good luck, the really old stuff truly sucks.