Just a idea, but if you install on the file server to a 40 GB partition and make the the balance of the drive D:.
So should you be using a 250 GB hdd that leaves about 210 GB that you Map for everyone to use and have sync toy backup D:\ at the end of the day, when computer is shutdown and the tray is removed. all should be backed up.
At this time put the tray to be used tomorrow in.