I'm very late to this thread, but in case others find it and are still looking for tips on remotely rebooting a headless Mac mini with FileVault, I did find one helpful hint. From a terminal window, you can enter:
sudo fdesetup authrestart
It will prompt for an administrator password, and the username and password to log into on reboot. In my experience, it doesn't actually log into that account, but it just leaves it prompting a password. More importantly for my purposes, it reboots without intervention to a point where screen sharing works again (and presumably ssh would too).
This obviously doesn't help with a cold boot from a powered-down state. For that I don't think there's any way to avoid connecting a keyboard and entering the password.