Thanks for all the suggestions. I may try the sun trick you suggested, John MacKenzie, when it's warm again. For now I think I'll try it in the oven at a low temp, and maybe that will help.

I'm aware that a significant loss in play quality is not only possible, but likely, however at the moment a few of them are so warped that the record arm cannot stay against the record -- the warp is so steep that it launches the needle airborne and skips significant portions of the first few tracks on the record.

BobL, there are a few neat things that come to mind with that. I've read a while ago (2015 or so) that technology was developed to digitize records just using a precision camera for cases where the original disk is rendered unplayable by conventional means, however that's likely still very expensive. There are, of course, audio engineers who could correct the tracks, but that is also prohibitively expensive, especially for some albums I'm listening to for fun more than anything else. Finally, I could record them myself and use a program to fix them, but in my experience, any changes I've attempted to make using Audacity have done more harm than good.

Gillymor, any chance you remember the temp and time you used?