I was up at the Rec Off today and searched the baptism register of Carew 1760 t0 1765 for the baptism of William James, ((I searched 3 times)) alas I failed to find anything of interest other than there are David, Benjamin and William James all having children baptised at Carew around the time of your interest.
I searched Monkton Baptism Register for 1768 to 1775 for the baptism of Ann Brunning at Monkton, alas again there was no mention of her, indeed no mention of the surname in the parish, I went on to look further and came up with the following ;
From my database of all parish registers for Pembroke St Mary 1714 to 1950’s from the mrge register which covers 1755 to 1802 I note ;
(Day lost) Nov. 1764 Joseph Brunning otp mrd Jane Bren otp by banns in front of Joseph Hughes. Both made their mark in the presence of William Froyn and James Harries
(Note William Froyn was parish clerk at this time).
From my complete transcription of the parish registers of Stackpole Elidor I note in the mrge register covering 1781 to 1812 the following
17 Oct 1789 William James of Stackpole Elidor mrd Anne Brunning of Stackpole Elidor by banns in fron of Henry Hood. Both made their mark in the presence of Thomas James and James Williams.
No doubt you have made reference to the St Twynells Mrge Register on the net and seen the mrge of John Brunning to Ann Owens 12 Oct 1782.
It is quite possible that John & Ann had a William bap 27 Jun 1784 at Bosh.
Alas this information does not give you Anne’s baptism, but it might come in useful for the future
Deep thought and inspiration required
Rgds
Orielbenfro
ORIEL a welsh window on a surname