After I rebooted the server, something new came up.
I rebooted the server last night, then let the backup job run normally. It completed successfully, then the next morning I tried to eject the USB drive. It wouldn't let me, so I removed the I$ share for that drive (using the Share and Storage Management program). Then, after running Process Explorer, I saw that VProSvc.exe still had a handle open on the drive. I tried ejecting the USB drive, but it still told me it was busy.
I tried stopping the Symantec System Recovery service, but it said the process was not accepting control messages at this time (paraphrased). I ended up killing the VProSvc and it then let me eject the USB drive.
I am wondering if SSR 2013 somehow hasn't fully let go of the drive letter/network share destination that I had previously told the backup job to save to, and that is causing the lock on the I: drive admin share. I am going to try manually assigning a different job letter to the hard drives so that they are all now the J: drive. I will see if I can unplug these drives successfully.