From the instructions for the application of the sandpaper to the drum, it appears you might have to toss the drum when the sandpaper becomes too dull to use. Maybe soaking it with mineral spirits might make the paper removable.
I'm sure there are alternative methods to mounting the sandpaper. Somewhere I have plans to a drum sander that used spiral wrapped strips that could be attached in a removable fashion. It's a good start, though.
The first reference I find to using lathe as drum sander was in FWW's "On Proven Shop Tips," page 112. Originally published in 1985. Have seen several versions over the years. Either ShopNotes, or Woodsmith, along with American Woodworker have published plans over the years. For paper attachment, use spiral wrap, with ends secured with fiber reinforced tape. After you cut first piece that FITS, remove it from drum and cut a template to match. No guess work on next piece, just lay template on it and cut to size. None of these ideas are mine, only remembered from other sources.