Let me update my summarization then:
For construction site work you can use Emlid Reach with FieldGenius (or equivalent) and localize with ~4 of the best site control points. Then you can do RTK work and have useable coordinates available in real time.
Thanks for your input @michaelL.
@tobias-dahms already mentioned ETRS/UTM33 but he is using free software and a PPK workflow. Does anyone else have a workflow for doing RTK work in a coordinate system other than WGS84?
The concern is not about the information you produce with your processed data, but more about how you or how your software deals with coordinate transformations, either before or after the RTK session.
Any input is welcome, even more info about PPK workflows. Additionally, does anyone know of any free software that does least squares fitting? Can QGIS accomplish the localization that @michaelL is talking about for PPK work?