After writing the above, I solved the problem, but decided to post it and the solution anyway in case someone else has the same issue.
Some more searching led me to this thread. As far as I could tell, nothing was locking the file, but when I tried to make a copy of the file, the copy process would error out, which led me to believe that perhaps the file was corrupted. I was, however, able to rename the file, and then ran a repair. Despite some of the horror stories I’ve read on here about database recreation taking forever, mine only took about an hour (my backup set is 250 GB).
After the repair, everything is working fine! 