How can I get files off of a Mac when the display is broken?
The simplest thing to do is boot the Mac in target mode (hold the T key down) and connect it via Thunderbolt or Firewire to another Mac so you can have visibility without repairing your Mac's screen. Alternatively, you could just remove the drive from the Mac and use a cheap $5 USB to SATA connector to mount the volume on a Mac to enter the Filevault passphrase to decrypt the volume.

Presumably, your system isn't booting since even in the blind, you should remember if you have to type in a user name and then press tab or return and then type the password.

User selection works by arrow keys and the space bar will select the user (and if you only have one user enabled to unlock the FileVault drive, you boot to a password screen so you only need to enter the password and press enter).

You can type the first letter of the user account and then type the password to get logged in. This assumes your user doesn't share a first letter with another account that is sorted before yours. In this case type the letter and then arrow key over to the second, third account and then type the password.