I thought I'd add this to the discussion as it may provide new information. I did read the thread and couldn't see anybody who had done what I did.
I built myself a Hackintosh out of Z87X-UD5H. I initially used the Intel 4600 graphics and with various combinations of GraphicsEnabler, npci and PCIRootUID got a booting system to 10.9.
I installed Multibeast and it seems to work very well.
I then installed a non-Apple 5770 card which also worked out the box. Life looked pretty good.
I then upgraded to 10.9.2 using the Apple store method. Yes I know, I should have used the Combo updater but it was late
I had the same issues as everybody else with the 5770 card not working after going through the Apple boot screen and a black display coming up. I looked through various threads, but couldn't really work out what voodoo combination might make my system work.
However I do have a real Mac Pro, an old 1,1, which is my daily workhorse. It has a genuine Apple 5770 in it. I had run both the Apple and non-Apple 5770 cards to try and speed up FCP X in my real Mac.
I pulled the Apple 5770 and shoved it in my Hackintosh and it appears to work OK. No issues on boot, FCP X appears to work well, and so far, so good. Now I'm not going to say its perfect and "works like a charm" and any of that nonsense as testing it will take a couple of days to validate that everything works OK, e.g. FCP X might throw something, Pixelmator may be a problem, VMWare Fusion might stop working, I haven't checked it with multiple monitors yet.
But what this shows me (and I have no doubt far cleverer than myself people had already realised) is that the issue with Mavericks and the non-apple 5770 and other ATI cards is due to the config of the non-Apple cards themselves rather than Mavericks. A genuine card works (at first checking) well with few or no issues to date.
I can't afford a new MacPro so will continue to validate that this Hackintosh is indeed viable. I also checked with a spare 660GTX card and that also works past the boot screen without going black, BUT the 660GTX is nowhere near as fast as the 5770 using FCP X though the 660GTX is far faster on every benchmark, real world experience shows its half the speed of the 5770 for what I need it for.
For me I might well keep the Apple 5770 in my Hackintosh as the Mac Pro 1,1 is getting long in the tooth and is not the fastest FCP X machine around. It may become an ESXI server as its eight cores and 16GB of memory or it might just go on eBay. Any offers