The original effects elements probably don't exist at this point.
Yeah, didn't an old friend of ours hear that Trumbull wound up throwing a lot of TMP vfx elements away because of space limitations around the time of BLADE RUNNER? That still puts the blame on Paramount, since they should have wanted all that stuff to store in-house to repurpose.
But that also explains why using stock elements in TWOK looked so bad in the theater, since I'm guessing they were just a copy from the TMP print rather than recomposited.
Recomposited TOS and theatrical TMP would be the bee's knees, that's for sure. And in this dimension I inhabit, about as likely as seeing Welles original cut of THE MAGNIFICENT AMBERSONS.
Something to consider as far as re-rendering the TMP cg at higher rez ... it don't look that hot in SD ... do you really want to see something that doesn't stand up to side-by-side comparison with the original model shots in SD to be viewed in HD? It's only going to point up the failings -- no, let's be generous, call it the limitations -- of the DE CG that much more.