The motherboard isn't where the droop is coming from though. It would take hundreds of amps to get a +12V power plane to considerably droop under DC loads.
It's the PCIe connector to edge connector interface that is the issue. The contacts are tiny, and while gold plated, tend to get dirty after a few insertions. One of the writers confirmed the 12+ supply was not drooping, and the +12V plane is good for 0.1v droop at most.
Just for reference, the PCIe spec (as of 2010 - sorry don't have the most recent) stipulates +12V ±8%, which is 11.04V to 12.96V @ the card.
Interestingly, @ 75W and 11.4V, you're burning 0.5V @ ~6.5A, giving 3W of heat in the connector! That's a lot! Look at the size of a 3W SMT resistor - they are huuggeee
EDIT: Used a PCB calc for a +12V "trace" to drop 0.1V under 6.5A of load over 100mm length (assuming normal copper weights, +15C temp rise). 4mm wide. A power plane would be 50mm average area after it's been cut by vias as a minimum