Old Style/New Style Calendars - Help Wanted!

I set out to write a post on Thomas Paine and his natal chart but hit a stumbling block on his birth date. One thing led to another and now my brain is suffering from what they call in the USA a "Charley horse".

Can anyone well-versed in both calendrical history and how it applies to astrology give me a hint or two please?

I understand the difference between Julian and Gregorian calendars and how & why the change was made. I spent around six years in my early working life working as assistant to our County's archivist, often assisting in the documentation of ancient records, where cross-overs of the calendar systems were involved. I'd have to remember how the start of the year changed from 25 March to 1 January in 1752 in Britain, and document any piece dated, say, January 29 1730 as January 29 1730/1.
I do "get" that part of the conundrum.

There's also the matter of 11 days difference between the two calendars for dates in the 1700s, which is a crucial piece of information when it comes to setting up a natal chart.

When looking at Thomas Paine's date of birth, January or February 1737 even Astrodatabank isn't certain whether the 29 January (Old Style) or 9 February (New Style) is correct because they are not certain whether the difference had already been accounted for when some biography or other quoted 29 January 1737. But.....here's where my brain cramps - shouldn't January 1737 be 1738 New Style? Or had it been adjusted from 1736 Old Style? And if 9 February is the adjusted date shouldn't that also be 1738 New Style....or.......?

And where were the Sun, Moon and planets really ? (Knocks head on desktop).

From source notes at Astrodatabank's page for Thomas Paine

Original entry gave January 29, 1737 at 11:30 AM, citing Dane Rudhyar with an added note of "PC gives February 9, 1737, 11:00 AM, spec." On Rodden's original typed file, she asks "is the date OS [Old Style] or NS [New Style] and notes that she "asked Blackwell 3/88." This seems not to have been resolved by Rodden. In December 2011 PT adds that England observed Old Style dates at the time of Paine's birth. However, reference works vary with both dates used (January 29 and February 9), depending on the source, often with no notation as to the calendar used. The date remains unresolved.

Any ideas, anyone, either about Thomas Paine's birth date/year or general advice for anyone interested in astrology when birth or event dates are affected by Julian/Gregorian calendar differences?