Yes, we contacted our web host about the problem and it looks like it was something on their end. Thanks so much for the help!
Yes, I double-checked the files, and I also tried deleting one of the files and re-uploading it (updating the link on the page) — no effect.
I’ll check into the permissions thing, although it seems like that would affect other files in the same folder, wouldn’t it? Why only EPUBs and not PDFs? (Not that I’m complaining, mind you!)