> there must be some way they handled it because something that said that it happened on a date that never occurred - sounds like what lawyers live for.

Yeah there are a lot of examples of dates being written two ways on the same document/artifact. In the Anglosphere there are two changes that happened close together: the movement of the new year from Lady Day to the first of January, and the Julian/Gregorian calendar jump, so that confounds things slightly. https://en.wikipedia.org/wiki/Old_Style_and_New_Style_dates