If there is no other solution ...maybe I would have to install a clean High Sierra using the ATI HD 4870, install web driver / enable remote access vnc, and then upgrade to Mojave?
This should work.
But before you try that, you may try.
1) Only install the Nvidia card in your cMP
2) Run the 10.14 installer
3) select a newly formatted drive as destination (for clean installation)
4) When it prompt for restart, shut it down
5) remove the Nvidia GPU
6) Install the HD4870
7) Turn on the cMP to let the OS installation continue.
There will be few possible outcome
A) OS installation completed, HD4870 can boot to desktop with just the Mac EFI. So, now you can install web driver and then swap the Nvidia GPU back in.
B) OS installation completed, but HD4870 only shows black screen once driver loaded. Then nothing you can do. But use your HS -> Mojave method
C) OS installation can't be completed, but going into a reboot loop / hang / crash. Then again, you have to use the HS - > Mojave method.
Anyway, no need to install web driver for HS. Simple make a clean installation with HD4870, activate VNC, then upgrade to Mojave should be enough. HOWEVER, this still very depends on if you can get VNC when the system still shows you the very initial setup screen right after OS installation (e.g. the screen that to ask if you want to send system info to the Apple server).
If that's the final part of the installation, and VNC cannot be activated until you make a choice, and really boot to desktop. Then your plan still won't work.