I see that you came to much the same conclusion while I was typing the above. Go for 18th century tunes (but don't pay any heed to the word 'ancient' in old collections of songs or tunes; many such were actually composed for the London theatres within the lifetimes of the people who supposed them old) and don't limit yourself to 'O'er the Moor'. The metre isn't that uncommon, and you don't as yet have any evidence for a connection.

Why 'ultimately Irish', incidentally?