Well, thanks kingfish!
I have wasted hours and hours to try get it working. Now I know that it really is Windows 10 which prevents me from using two different drivers for my two different graphic cards.
My only comfort is that Nvidia users are facing the same problems.
I resolved this issue by going back to Windows 7, which will be end of life in year 2020. I guess Microsoft is not interested in MY personal data, since they force me to continue using Windows 7.
pokester I've already tried all that DDU stuff but tried again a few times in hopes something changed more recently, still a fail. Also just an fyi, but the fast startup setting doesn't affect restarts, shouldn't have any bearing on this. I never use hibernate either, always off. Well, the most recent driver package I can install remains as 184.108.40.206.
goodplay I misspoke on Error 99. That's actually just an error regarding a driver without a digital sig. In this case I think it happens because the install process hangs and the restart happens before the driver registers. For example, if I try to install a newer driver package beyond 220.127.116.11, get the hang and restart into safe mode and try installing a different driver (without removing what's there via Device Manager or DDU), that's when Error 99 pops up. I think that's pretty much irrelevant to what's actually causing the drivers to fail installing in the first place though.
If your GPU is from sub vendor HP, then we might have had the same issue. I came to the conclusion that there is an issue with the stock BIOS for HP's AMD R9 390X causing the driver install to fail and the system to hang.
I have created a custom BIOS for the AMD R9 390X HP OEM. I used an XFX BIOS (XFX.R9390X.8192.150612.rom) and updated fan and other settings to be equal to the original HP one.
I have flashed it and the GPU is working fine now. AMD drivers were updated to the latest version "Win10-Radeon-Software-Adrenalin-2020-Edition-20.5.1-June10", 27.20.1017.1011.
A link to the modified ROM below. Use at own risk.
HP AMD Radeon R9 390X 113-C67132-104 - fixed
Output from GPU-Z: