Well, I had a chat with the very nice Welsh lady today and she confirmed that when she did the search for me it was a) with a five year leeway, b) covered all possible spellings (Harry, Harris and Harries) and only came up with the two aforementioned Anns, both of which had fathers named David who were Farmers, and both of which were born in Llangyndeirn.
She offered to have another poke around this afternoon in case she had missed something, but as there is no email from her tonight then presumably that is that.
It rather looks as if I have come to a dead end with this one, because even if I sent for both certs I would still not have a clue which was the right one.
Irritating in the extreme.
thank you Kite and Merry for helping