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.
It worked! with only one difference:
1) First I installed the Nvidia card (GTX970),
2) [HS-10.13.6 / FW-138.0.0.0.0] I ran the Mojave installer and selected a secondary newly formatted drive as destination (clean installation).
3) It restarted, but I did not change the graphic card. I waited about 1+ hour (with black screen) for the installation to complete, listening the sounds of the Mac. Basically I calculated a considerable time, and when I thought that the screen would already be in the initial configuration, I turned off the mac, switched the Nvidia to the ATI HD4870 and booted again.
5) YEAH! I could see display on Mojave with ATI HD4870, and also it showed me again the pending initial mojave configuration.
6) I did the initial configuration, and enabled the remote access to be able to view the screen from another mac (VNC). (I did not install any web driver)
7) I turned off the mac, switched again the ATI HD4870 to the Nvidia and done! I just have to wait for the Web Driver release for Mojave, and install it using VNC. While I'm on the HS disk.
Thanks for the idea!
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