The issue seems to have been related to secure boot.
I hadn't set an admin password in my BIOS, which I suppose was required? So while I had disabled secure boot at some point in the past, this specific setting had been reset or was being ignored by the lack of an admin pass.
Setting the password solved the issue.
Windows 10 has an issue with it's driver enumerators, not just for some display combinations, but Realtek audio and some Bluetooth as well. The've been slowly...very slowly..working it out. Until they handle it, or someone else figures it out, the easiest solution is to change drivers whenever you change devices, manually. Don't listen to what you're told, ...
First thing first. Backup your important files before venturing further.
To add a PPA to eOS you need to install:
sudo apt install software-properties-common
Next thing is to add a PPA which contains driver for intel:
sudo add-apt-repository ppa:oibaf/graphics-drivers
sudo apt update
Now getting the latest intel driver:
sudo apt install xserver-xorg-...