Pretty ingenious workaround. Just a note to skip some of the first 'blind' section (installing openssh server through the desktop environment with no screen visible):

Ctrl+Alt+F1 still works in many distros to switch VTs to a text-mode terminal tty1, and likely also works without logging into the desktop. Ctrl-Alt-F7 to switch back.

From here, you should be able to login blind, then sudo apt install openssh-server (assuming Internet connectivity,) or kill whatever misbehaving process, or even restart the whole DE or computer.