I had this issue. I found turning ON PCIE power management in the BIOS solved it.
Can you tell us what settings you used for power management? I'm using a Sapphire 5700 XT Nitro+ and a GA-Z97X-UD3H-BK motherboard with 4 options when I turn on Platform Power Management:
• PEG ASPM (Default: Auto)
• PCIe ASPM (Default: Auto)
• CPU DMI Link ASPM Control (Default: L0sL1)
• PCH DMI Link ASPM Control (Default: Enabled)
I've disabled all except left PCIe ASPM to Auto. First difference I've noticed is that when I move my mouse cursor during a screensaver; it responds immediately. Before it would flicker a couple times. I'm running Big Sur 11.1 on OpenCore 0.6.5 with a 4790K processor and 16GB RAM (in their correct slots).
I've been having random freezing, black screens and reboots all the time. Sometimes they occur when idle, other times when loading a YouTube video, sometimes before a game loads in steam but MOST often after a game has finished playing and it tries to go into the main menu. (using GRID: Autosport benchmark to test this).
I hope this change fixes it. I've tried changing SMBIOS from 15,1 to 14,4 and iMac Pro 1,1; nothing has helped. Only other thing I can think at this point is to try agpminjector kext with Platform Power Management turned on and off.
Removing the 5700 XT and running only with the HD 4600 iGPU makes the Hackintosh run perfectly, logging into the OS also proved seamless but with the 5700 XT the screen does go black ONCE when entering my account password.