A wee update from me - not that I have found anything definite, but I finally got around to doing a DNA test, and I chose (for my first shot anyway) to get an ancestry autosomal test, mainly because they have the biggest database.
I have listed as likely 3rd cousins, 2 I think sisters (from comparing their trees), The confidence level is extremely high, one has 123 centimorgans in common, over 6 segments of DNA. From what I have read, they are a certainty (just about) to be a direct connection at 3rd/4th cousin level, probably 3rd cousin level.
On top of that they have all the right names, Burke, Michael Burke, even Miles Burke, marriages to Connolly - but I just don't see where they fit in with what I know! And they have not responded to my message!
There are also 3 other 4th Cousin connections, but again no easy fit into their trees. 4 of the 5 tree's are US based (from memory) the last one is in Australia, with, as far as I know at the minute, no one still in Ireland.
I will have to look for one of those 'free weekends' that ancestry do around the holiday seasons, and see what I can find. Or take a deep breath and look at Family search a bit more deeply. I find it hard-going!
PS Any suggestions welcome and gratefully received!
PPS I lost the will to live searching the catholic parish records, but, you're right, I should go back and finish it some day!!