Something isn't right about the pictures. First, burn mark doesn't start from the PCB. You have 2 cards, the lower cover of the top card is melted, but clearly it was melted from outside to inside, indicating the source is from outside. Then you have the lower card, those are plastic burns from the top card, again not from inside to outside. The location of the GPU, VRM and RAM looks perfectly fine, indicating the abnormal temp from these components can be ruled out. But if the fire didn't start from the PCB on the TOP and BOTTOM, then what causes the burn?
You said you SLI, why do you place the card back to back where you really should populated socket 1 and 3?
Edit: I really mean PCIe 1 and 4, as I mistakenly think that the second PCIe was a PCI.
Suppose the origination is indeed on the video card, then it means there exists some components that were so hot that melted the cover of the top card from the back side of the second card, but there are actually nothing on the PCB located at the lower part of the card.
Picture from hardwareheaven.com
Here is the interesting part, look at the light plastic mark on the back of the second card where the GPU is, it seems to be from the plastic at the bottom and got spun to the top. Indicating the fan of the top card works. Look at the blade of the top card, the tips are also darkened, supporting my theory. That the fire didn't start off from the card, but there were sitting on top of something that melted the cover of the top card. Now look at the mobo pic
The clip of socket 3
Edit, again I meant the 4th PCIe slot, not 3rd. was narrowed, indicating OP couldn't have a populated that slot during the incident. Look at the HS on the mobo, it actually matches the melt part of the top card, indicating it was extremely hot during the incident. From the picture I say the mobo temp is way over 100c during the incident, but why didn't heat got vented?
Because the back side of the 2nd card is blocked the intake of the first card. It was spinning, but not moving air!
There were 2 things that are hot, the top card and the HS on top of NB. In conjunction with the fact that intake of the top card is blocked, temperature at the surface of the NB HS gets so high that it melted the bottom of the top video card's HS's cover.
First, these video cards are not meant to be placed back to back as those ain't centrifugal fan, it require open space for the intake to work properly. Even with a blocked fan, it couldn't cause this, since the GPU will cease to function when it is too hot, but the GPU wasn't too hot at the time, I am saying this out loud but the GPU as well as the HS reached around 100c which is not enough to trigger the temperature production of the video card, but there is another source of heat, the HS off the mobo, making the bottom part of the card exceed plastic melting point. Here is something interesting i found from an old review about that particular mobo,
GA-X58A-UD5, from overclock.net.
Whenever a heatsink gets hot you know it’s doing its job, and well the gigabyte heatsinks get very hot, yet we never see Northbridge temperatures above 40C at stock and 50C overclocked, that is without supporting fans cooling everything down, but the heatsink temperature is another story, measured at stock load the heatsinks get up to about 70C and at overclock about 80-90C if you average them all out, the most heat ends up at the Northbridge cooler as its where all the heat pipes meet, and the cooler is perfect for a small 40mm or 60mm fan, yet gigabyte does not provide one, because it isn’t really necessary with the north bridge temperatures being that low. It would have been nice though. As you can see the heat moves from the block to the fins, on the UD7 on top of the fins is a waterblock, not the most effective way to design a cooling apparatus, but easy to implement because you can switch out the waterblock for the “silent hybrid” heat pipe apparatus the UD5 does not come with and the UD7 and UD9 do get.
So, it isn't the video card, PSU or the mobo, but the combination of 3 factors, 1) intake of the top card is blocked, 2) extremely hot NB HS (lack of NB fan), and 3) poor case ventilation. Look again at the third PCIe slot, there are no burning plastic, but are de-shaped, indicating that temperature was so high that it actually melted it.
Here is my guess, OP's goal is a ultra quiet PC, thus use H50 without OC. There may be 1 outtake near the mobo which is set very low because of the noise and it really doesn't move hot air. The airflow at the lower part of the case is next to completely dead except for the second card. The temp of the first card is high, near 90c, but OP didn't pay attention about it. Unfortunately, there are no thermometer at the point of ignition as therefore OP didn't even know there exists a vent problem.