I talked this unpassant before into other threads, but never talked about this here.
Some time ago, a user got in contact with me about a Mac Pro that couldn't work with NVIDIA Titan cards. The user had 5+ MPs and Titan cards and one of the Mac Pros never detected the GPU, but the card worked into any other Mac Pros and the Mac Pro worked perfectly with GT120 and AMD GPUs. Since this was a weird one, I asked for the BootROM dump to analyse it.
I found that the 1st and 2nd streams were almost full and with a weird binary blob into it. I extracted the LBSN_BD sector and all the hardwareIDs, injected into the generic 140.0.0.0.0 and the user flashed the reconstructed BootROM into the problematic Mac Pro. With the reconstructed BootROM, the Titan card worked. I was surprised and thought that was just a fluke.
After that, 3 different users got into contact about Titan GPUs, 2 of them had the same NVRAM problem and the reconstructed BootROM worked, with just one the problem was with the backplane.
So, if you have video not working with high-end NVIDIA GPUs, maybe your problem is related to 1st/2nd stream corruption of the NVRAM.
Another thing, this problem seems more common with earlier MP4,1, the ones with Base_17/18/19, but one Mac Pro was a mid-2012 made late 2013, one of the last ones.