EB online is not of substandard quality. But it is written for people to read, not bots. EB online, the Dictionary of National Biography, and other quality sources place upon the reader the responsibility of understanding what calendar was in effect at the time and place of an event, and interpreting the date accordingly. A bot that cannot fulfill that responsibility is functionally illiterate and should not be allowed to read quality sources.
In the Edward Nicholas and Cromwell examples I looked at the sources. Being a literate human being, I interpreted the dates as being Julian calendar dates, and changed the Wikidata calendars from Gregorian to Julian.
Similarly, I corrected the entries for Cromwell by swapping the birth and death dates, and changing the calendars from Gregorian to Julian. (I was misreading the dates, they were not swapped after all.)
For Edward Nicholas, I hadn't seen enough SNAC examples to infer what their date policy was, so I just deleted it. I could see that there was a perfectly adequate reference to the Dictionary of National Biography, but that whoever had used that source did not understand their date convention, so the calendar would have to be corrected. Now that I've seen more SNAC examples, I infer their date convention is similar to Dictionary of National Biography.
As for an earlier cutoff date, you might be able to consider the source. If you know the source only describes people from a certain country, you could use the cutoff date for that country.
Using 1583 would be a bad choice. Large numbers of items come from either the English or Russian Wikipedias, which in turn concentrate on people from those countries. Russia adopted the Gregorian calendar on 14 February 1918 and England and its colonies adopted it on 14 September 1752.