HTDP uses 14-parameter transformations, exclusively, to transform positional coordinates between spatial reference frames. Thus, HTDP addresses only the coordinate differences associated with differences in the origin, orientation, and scale between reference frames and/or differences in the rate of change of these features with respect to time.
As a result, HTDP is not intended to perform rigorous transformations between the various realizations of NAD_83.
Coordinate transformations between the various realizations of NAD_83 can instead be performed using the tools NADCON (for 2-D transformations) and GEOCON/GEOCON11 (for 3-D transformations).