However, I could barebones it as you suggest. The fans and GPU could be introducing noise, and that would be the only way to reasonably question the motherboard.
Confirm it is the GPU.
Turning up chassis+CPU fans to max did not introduce noise.
Turning up GPU fan to max did not introduce noise.
Running Prime95 to run the CPU at 100% did not introduce noise.
Running Video Card Stability Test (link) brings the noise.
Turning on Noise Reduction does remove it, however this reduces the quality of my recorded voice as the noise is in the same range as my voice.
Now the question is can I mitigate it by changing slots? I'll shut down and find out now.
Edit: No, the noise still persists even with the x1 slot.
I'm out of options for this sound card. It's an incredible product but for me it doesn't look like an internal card is going to be an option for this build. Perhaps I will have to suffer using an Omni (SB1560) or Xonar U7.