Trying a different cable and a different monitor will at least rule that out. Then things definitely point to the MB. It might just be coincidence that when you stress the GPU, the monitor is failing. Main thing is to rule everything else out as it would be so frustrating to swap out the MB only to find the problem still exists once you get everything back together.
Another suggestion: remove the graphics card from your system altogether and run the graphics from the MB graphics port. Depending on your CPU this should be possible. The BIOS should detect this but if not, you may need to reset BIOS to defaults so that it can identify the correct graphics port to use. If that works OK and you have eliminated the graphics card as a culprit, all eyes are unfortunately back on the MB being the problem.
Intel Core i7-4770K @ 4.4 GHz / EVGA GTX780 Superclocked / Corsair Vengeance DDR3-2400 MHz RAM 16GB / Asus Maximus Hero VI Motherboard / Corsair HX1050W PSU / Corsair H100i closed loop water cooler / LG Blu Ray DVD CD writer, Asus PB278 Monitor 2560x1440 / Logitech G110 KB / R.A.T. 5 Mouse, Samsung EVO 850 500 GB SSD / Samsung EVO 850 256GB SSD / Seagate 7200 RPM 2 TB HDD / Windows 10 Professional x64