I'm not a surveyor, but was the IT guy & supervisor for a city's two-engineer surveying team as we went GIS... Basically you fudge it. Precision losses, errors

I'm not a surveyor, but was the IT guy & supervisor for a city's two-engineer surveying team as we went GIS... Basically you fudge it. Precision losses, errors, and local ground movements swamp continental drift. As you noted, some of the original sources go back over 100 years. A huge, huge amount of the surveyor's time was spent cleaning up data. One of the steps was to map the vectors around a plat. There was always some kind of closure error when you get back to the beginning position. The surveyor's job was to tweak the points to resolve the error. Kind of like auto body work; he used a lot of skill and experience in making the most seamless repair possible. (The most important part of my job was running interference for him, nobody understood why it took so long to "just digitize some maps".) In general the original surveying records remain the source of truth, and the maps we produced with the tweaked coordinates were working documents. To be technically correct, another map would have to go back to the original documents and re-apply corrections. IIRC for some really egregious problems there were ways for the surveyor to amend the official truth. Automating or re-implementing legacy systems is always a horribly messy data-cleansing exercise, but I think this was the most mind-numbing, tedious, endless slog I've ever been involved with.