score:7
I finally tracked down what seems to be a copy of the letter that I think you are referring to on Find a Grave. The extract of the relevant section is here:
The text reads:
A testimony concerning that Faithful Servant of the Lord, & my Dear Friend and Kinsman Cuthbert Hayhurst, who was born at Easington in Bolland in the County of York in Old-England & departed this life, at his own house in the County of Bucks abt the 5th of the first mo 1682/3 near the fiftieth year of his age.”
The '1682/3' is a reference to the fact that the start of the legal New Year was commonly on Lady Day (25 March) in many places (including England and British dominions), and 1 January elsewhere (Scotland had changed its calendar year to begin on 1 January in 1600). Pitt (as was fairly common with letter writers at the time) used the dual-year format to account for this.
In England New Year's Day was changed to 1 January in 1752, when the Gregorian Calendar was adopted.
As you note, the Calendar Act introduced the Gregorian Calendar in Great Britain and British dominions in 1752.
What is, perhaps, less well-known is that the Act also changed the start of the legal New Year in England and the British Dominions to 1 January rather than 25 March (Lady Day), which had previously been the start of the legal New Year since 1155.