I figured it out. There was an unconventional abbreviation of the HARN based projection in the TIFF's header information that didn't seem to migrate well to the SID's header, leading ArcMap to interpret it as a 'Custom' projection. The alignment issues seem to have arisen from truncated/rounded parameter values in this 'custom' projection being read from the SID's header, compared to the predefined NAD83_HARN projection paremeter being used with the TIFFs.