A total station would be super helpful, I agree, but unfortunately, I have neither the storage, nor time to devote to learning it fully (I only have a basic knowledge of it), whereas I am much better equipped for GPS data and GIS analysis. Because I will primarily be dealing with historic buildings and not necessarily archaeological sites, I am not as worried about the lack of a total station.
The Emlid open source hardware looks particularly interesting! I appreciate all the recommendations so far.