Trying to get my new 5700XT to work, but gets a black screen. Trying to install with iGPU, but gets a white screen

I've been running my following hackintosh very stable for several years, with a 1070 and High Sierra:
- Gigabyte z97x gaming 5
- 4790k
- Palit gtx 1070

However, I decided to get me a new Sapphire 5700 XT and install Catalina instead, but ran in to quite a lot of problems...

I made the usb-installer using the vanilla method listed here in the sidebar. If I try to boot with the 5700xt (using hdmi) I get stuck on a black screen after the apple logo and the progress bar. I've tried both with and without whatevergreen 1.3.5 kext, same result.

So I unplugged the power from the 5700xt, enabled iGPU in BIOS, and tried to install with internal graphics instead. That got me all the way through the Catalina installer, the language selection, but after the final reboot I get stuck on a white screen, only seeing the mouse cursor. I think the "Welcome screen" is supposed to be shown there.

I've been stuck here for a couple of days now, and could really use some pointers on where to troubleshoot :-/