When you say "gutting it", what are you referring to exactly? Are you saying you just want to keep the case and replace all the insides? Is there a reason you want it to be this small?
What country are you shopping in and what's your actual budget.
There will be some issues inserting a "standard" mITX board that has a 24-pin power connector when the proprietary PSU inside that case only has a 4-pin and an 8 pin with very specialized cable lengths. Also, "standard" motherboards have a standard size/shape IO cluster in the back. The mobo in your 780 USFF is not standard. How much "case customization" are you open to? Measure the PSU, how close is it to
this one? (3.2"x1.6"x5.9")
9.4"x2.6"x9.3" is pretty small, but do-able for a replacement. That's about the size of an Antec ISK 110. You'd be looking at an external (laptop-style) power supply.