Spent quite some time struggling with the same. 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: