KingLucius I don't have a HDMI monitor or TV, (my TV set is still a 60kg CRT) and I don't have the same GPU as you do.
All I can advise if you have problem with HDMI is to first boot, update your system, etc. without connecting the monitor, then when everything is up-to-date and working fine, you can try to connect it and reboot.
If you install the nvidia drivers, make sure DoFlicky selects the nvidia-390-glx-driver
Personally when I do a google search, I found plenty of results with nouveau not detecting HDMI monitors and many of them are SOLVED, I am pretty sure some of the solutions should work for you since nouveau does support HDMI.