Assuming that the survey point has a datasheet (adjusted control), this would be good head-start for occupying that point with a Base. The RTK Rover Solutions would inherit the same Reference Frame, Epoch, etc as the control if you use the published coordinates at your Base.
However, I don’t see many good choices for the area though on the NGS Data Explorer 
If you’re not talking about 1 of the 3 Triangulation Stations, then you might as well Survey-In a Base and overwrite the Elevation from the datasheet for a “vertical-only” tie basically.
Considering your location/situation, you also might consider the StarLink thread for RTK via NTRIP ?