I've actually come up with what I think is the best solution to this problem, but wasn't sure if it should be here or in "Tips and Tricks." So I'll post it here.
My external drive enclosure has a known issue with APFS formatted SSDs, where they would eject randomly without user intervention. So I converted all my volumes back to HFS+ via copying files to an external drive and back again. This broke the link to my external Logic Sound Library, in spite of the volume having the same name and file structure. Making a new alias to the Application Support folder on my boot drive obviously wouldn't work, but neither did making a symbolic link.
I didn't want to download the whole sound library again (which is what I ended up doing after the last time something like this happened), so instead I copied the Logic and Garageband files from External/Library/Application support back to Boot/Library/Application Support. I also copied the contents of External/Library/Caches/ back to it's corresponding location on Boot/Library/Caches. (This all assumes you have free space on your boot drive to do this. Not having enough space will obviously make this fix more complicated.)
I started up LPX again, and it said it needed to download the essential sound library, so I let it do that (1.18 GB, not a big deal). And everything was back in order in terms of LPX built-in samples. I told Logic to relocate my library back to the drive it used to be on (after deleted my old library folder), and I didn't have to download the whole library again. All told it took me about 10 minutes to do, instead of several hours.