If you need to boot into the Recovery Partition, you're gonna have to have a keyboard and screen to see what you're doing...
2nd Edit: I didn't exactly read it right. You still need to access the GUI to do the steps on this page. I would just try to find a keyboard and screen .
EDIT: Looks like there is a command line interface (tmutil) for restoring TM backups, if you could SSH into your server you could give it a try: