Hi Austin,
sorry for the delay here - the holiday season...
The survey you performed with the Trimble R8 - which software did you use here?
A height offset of 111.8 sounds like an applied geoid.
GCP (and/ via) TMM apply a time dependent datum transformation which adjust for stuff like tectonic plate movement - TMM does not apply geoids at the moment.
Those adjustments are important if you mix correction sources - like SBAS and/ or Trimble RTX and/ or VRS/ RTK stuff.
The system NAD83 is a composition of things - if you go here: EPSG Geodetic Parameter Registry and search for 'NAD83' you'll find a whole lot of matches plus. If you open one of those (say EPSG::6319) you'll see a section about 'Geodetic Datum' and potentially (depending on the epsg) an applied geoid.
I'd guess you have an applied geoid while GCP provides ellipsoidal heights.
Regards
Nico