I just wanted to be a good forum user and post that I isolated my hang problems to the RAM as was suggested. I ran the ubuntu memtest86 and it found large blocks of errors in my original G.SKILL 2x8GB RAM. I replaced the RAM with CORSAIR VENGEANCE 2x8GB 1600MHz DDR3 ram and all the memtest86 tests pass now. Windows PE loads fine and many of the stability issues I was seeing disappeared.
I also switched the BIOS fan speed to "cool" just to be on the safe side. The NUC runs much cooler now and it is still essentially silent.