Doesn’t look like Intel released a 6th gen I7 version of the NUC. Im guessing there will be an i7 version later this year with the next chip releases. I looked at some benchmarks to compare the older i7 NUC with the current i5 NUC and they are pretty much neck and neck.
As far as performance goes i think it should be just fine but honestly you have a whole lot more files than i do (im at 400gb or ~14k tracks). See @brian 's post here. His opinion is certainly better than mine with that large of a library.
If there are performance concerns the same company sells these. I know its above your budget, and honestly starting to get pricey but a full quad-core i5-6600 processor should easily have enough power, well above an i7 used in laptops.