Do you have any of the "real" locations for any of these points? Or can you share more about the data, what it's representing?
We once received a dataset where the data was almost in State Plane coordinates, but they all had been shifted by the same amount. Essentially, this particular surveyor used their own personal origin for the state plane grid, which was highly unusual, but once we knew the amount things had been shifted, it was simple enough to get them in the right place.
- Josh Carlson
Kendall County GIS