How to get my screen responding again?
Since you can ssh into the box, you can start killing processes one by one and eventually you will either reboot the box or free up the item that's holding the CPU / GUI frozen.

I would probably do these things in order of severity:


Start a time machine backup before killing anything tmutil startbackup --block --rotation
If I don't care to save work (since this kills all apps abruptly) - kill the loginwindow process and log back in.
If I do care to save some work, kill all user processes not belonging to the user that needs to save work.
Then kill all user processes that don't need work saved. (Apps and such)
Then use AppleScript to tell each app that needs to save work to quit. (assuming the GUI isn't responsive at this point)



  osascript -e 'quit app "Take Five" '


At this point, you'll either need to list the specific apps that you need to save work and ask if there are any ways to force a save (perhaps they use autosave and will recover all work anyhow) or just issue a restart / reboot command and get on with using the machine and recover what you can from your last backup.