So, my whole point of getting the RX580 was to upgrade to Mojave beta. Unfortunately, I had the beta 3 full installer which didn't have the latest FW version 89 (I was at 87), and after booting to Mojave for the first time, the automatic OS update system installed beta 4.
Thus began my odyssey of FW upgrading post RX580 install. When I initiated it by launching the beta 4 full installer, I forgot to swap in my 5870 and was met with the unending black screen. I had to repeat the whole process from the beginning but swapped in the 5870 while it was shutdown. The FW update was successful and rebooted to Mojave, surprising me with the fact that Mojave was able to run with the 5870, albeit with some graphical glitches here and there, but nothing significant that prevents its use.
Feeling like now was finally the time to try booting into my UEFI Windows 10 Pro partition (Apricorn Velocity Duo x2 using a pair of 2TB 850's hardware RAID'd, with the first partition NTFS) under my new 580, this is when things got ugly.
1) I used Paragon NTFS to boot to Win10 but after a period of time in a black screen, it rebooted again and was greeted with no boot device found. Without the boot screen picker, there was nothing I could do to prevent always getting to this screen: I tried PRAM reset, pulling all Windows drives, pulling all drives. But the Mac always booted to this message.
2) I swapped the 5870 back in to use the boot screen picker to properly pick my Win10 partition, which is labelled "EFI Boot" on this screen, and was finally able to run Win10. I suspect the Paragon NTFS startup manager (which I have never needed to use before) doesn't properly select the Win10 boot partition (it doesn't show "EFI Boot" but the actual name of the partition).
3) Verifying that Win10 was now the startup disk by rebooting, I shutdown, swapped in the 580 then powered up. Unending black screen. Forced a power down, then powered on and waited: nothing but black screen. Again just couldn't would get away from that black screen despite all my attempts. I reinstalled the 5870 and it booted just fine into Win10 and Mojave. I then tried to pre-install drivers from the 580's install CD, but without it physically installed, there is no way I could get the drivers to install (without an external power source, I can't install and power both the 580 and 5870).
After pulling and reinstalling my 580 about a dozen times, I'm now an expert in throwing that puppy in almost effortlessly... but at present I have no way to boot into my existing UEFI Win10 partition under the 580.
I will try doing a brand new Win10 install under the 580 on a spare drive when I have the time, but I'm open to suggestions until then.