So I've recently been annoyed at the inherent limit of my Cort Yorktown, in how high I can go up the fretboard before my thumb has to start doing weird things. I've attached a small video just to demonstrate. 

As I get to the highest frets, my thumb has to actually go beneath the fretboard, because the neck heel is so thick. It makes it hard, at least for me, to play fast and smoothly. It's a semi-hollowbody, so I understand there's not much one can do besides perhaps shaving down the heel. 

But has anyone else encountered this problem on this type of guitar? Shave the heel? Play an octave down and substitute the pitch with an octave pedal? Use another guitar? Just wondering what your guys' thoughts might be.

That seems pretty standard for that type of guitar. You should move your thumb so it's touching just the bottom back of the fretboard.
Prs se Holcomb is the answer
Doncha just love clunky neck heels? You either get to love putting your thumb wherever it can go on the body of the guitar or you buy a guitar with virtually no neck heel. This is a semi-hollow with a smoother neck heel (from Carvin):

LP-style guitars with shaved neck heels (Gibson Axcess Custom on the right, Agile custom on the left):