For paperbacks torn at the binding the most convenient thing is probably just an acid-free archival transparent tape, like Scotch 845; that won’t restore in the sense of a book collector, but will make the book usable again and won’t yellow. For hardbacks the usual spine repairs involve archival PVA and bookbinder-grade buckram cloth, but the latter is surprisingly hard to source in non-library quantities unless you’re happy to do all your books in one color. (As it happens, I expect some gray buckram in tomorrow’s mail to repair some old textbooks I’ve overused.)
You used to be able to pick up quite good turntables cheap on eBay (my vintage Thorens was under $100), but prices have been really climbing as people with too much money have decided they need a turntable as room decoration. Rumor has it that Pokeman Go has made it even worse (since you can apparently use a turntable somehow in playing).
Back when taping on the first or second play was popular, reasonably good turntables were easy to find. Not super fancy or anything, but good enough not to wreck your records and, as you say, track at a gram or two. And every 16-year-old knew how to set one up.
Now, when taping because your stylus might wreck your record is no longer a thing, the world is awash in turntables that can probably wreck your records. Then again, most new vinyl comes with a download or even a CD in the sleeve (unless you’re buying records by the Beatles or Bowie, in which case you get your vinyl and that’s it)…
To make it clear-- playing the “glue skin” would produce sound, perhaps even something recognizable as what was on the record, but there are some caveats here. Ignoring the softness of the dried glue, and assuming the grooves were cut close enough together that the needle will ride the resulting ‘negative groove’, you would actually be playing part of two different sections of audio simultaneously: half of one portion of groove, half of a portion one rotation away. The audio data is contained in the ‘ridge’ now, so by being in between two ridges you are playing part of two different bits of music. If this was a 12-inch single where the grooves (or groove, since it’s one long spiral) were cut farther apart then the needle would probably just play half of that audio, the force of the spinning record holding the stylus against one side of the ridge only.
Plus, part of the audio data cut into the groove is depth-related, which I think would be lost by playing the negative image. The groove would be backwards too, so you would have to start the needle at the center and have it move towards the outside, playing the audio backwards, unless you have a turntable with a reverse button (they do exist.)
I take your point, but I had in mind something involving digitising laser reflections off the positive image, incorporating plentiful amounts of handwaving. Conversion to analogue handwaving, naturally, for that unmistakable warmth of tone.