I have seen no calendar problems post a very few years after 1751 - in fact many people were using the new style before the official changeover. I'd be very interested for any use of the old style calender say after 1755 other than in the context of folk customs - I have seen none, though obviously old folk state that the year should begin on Mar 25th and that Christmas should be celebrated later.

Look at the dates mentioned Mathew wrote 29 Oct 1771 when Henry is sick (and from Henry's own will required a nurse but only £3 so probably a few months) - Matthew dies in December of that year - by the time of probate of Mathew's will Henry would appear to be dead which fits in with an 11th Feb 1772 burial. I personally checked the register at least as far as a few months earlier (judging from my notes) - I will go back and check but again but I'm pretty confident he was buried in 1772. The key with these calendar changes (around 1750-1753) is to look at the sequence in the register.
I'm not criticising Donna (or John Robinson) but obviously with no sources it is somewhat difficult to check. If Henry had just fathered a child (from it would seem his deathbed) I would have expected him to make some reference (and provision) for that child - there would I suspect also be a claim against his estate by the mother