It looks like it is working. I can now eject the I: drive without the handles from SSR/Windows share being open on the drive. I eventually had to:
1) delete the existing backup job
2) delete all external USB drives from the Advanced menu -> Drives list
3) go into Tasks -> Options -> Settings -> General -> Default backup destination, delete that entry out completely and click "OK"
(I also went to Tasks -> Manage Backup Destinations... and deleted out as many entries from there as I could, however I don't think that helped.)
4) shut down the SSR service and kill the VProTray.exe process
5) change the drive letter assignment of the USB hard drive I wanted to use from I: to J: using Disk Management admin tool
6) safely eject the USB drive (J:)
7) restart the SSR service and run the VProTray.exe process
8) plug in the same USB drive again and assign the drive letter I: manually
9) create a new backup job and choose the default location to be the I: drive, along with all the other settings (backup recovery set, new recovery point weekly, M-F repeat)
I will run backups on this for a few days and see if it allows me to 1) eject the drives without a problem and 2) plug in a new hard drive (ie, [Tuesday]) and have the job backup to that drive (because there had been a problem where the backup was pointing at a drive label, not a drive letter, and failing because that drive label wasn't present).