I've narrowed down the issue and it doesn't seem BIOS related after all.
It seems to be related to the HDMI output vs. DP output as well as the NVIDIA driver with shutdown vs. restart.
In Linux Mint 19.1 with the official NVIDIA driver 430.14, if I reboot the system then the displays will work normally. If I instead shutdown then the displays won't work during the BIOS boot stage but they come back after loading into X. Also, if I connect the monitors with HDMI instead of DP then they work whether the system was restarted or shutdown.
Strange right?