The NGS has been telling us for YEARS that if we REALLY want to convert NAD27 to NAD83 (any flavor/realization), that we REALLY NEED to go back to the original OBSERVATIONS and reprocess the data using NAD83 constraints.
It really doesn't matter whether the “original observations” were T2 Triangulation, theodolite/EDMI traverse, transit & chain, or GPS...they were ALL observed on (or near) the surface of the Earth, and that hasn't changed all that much in the last thousand years (except of course where it HAS).
Even in those cases (quite common actually) where the original observations are NOT available, one “can” reverse-engineer most data-sets in such a way that reasonably good spatial results can be obtained. You can't make a silk purse out of a sow's ear, but you can improve on most (if not all) easy-button techniques.
Loyal