Got my replacement external hard drive and restored a backup onto it. And everything is back in order.
Except my iTunes library:
My iPhone was very happy to have iTunes open and immediately tried to sync, which produced a string of messages about missing files. None of them were actually missing, they just weren’t where iTunes was looking for them. And it tunes out those half dozen files weren’t the only ones.
Fortunately, this was a relatively easy fix. If you change the default location for your iTunes Library and it ever becomes inaccessible, iTunes will revert to the default. Resetting that and letting iTunes “clean up” almost completely fixed this issue. The exception seems to be some files that have an extraneous “localhost” appended to their location. I’m not sure what caused that particular issue but it was only a very small number of files and, amusingly, none of them from that six-days-long list.
Nonetheless, it’s no wonder I have a wicked migraine. Joy.