did you get any more info re Hyde, Martin? And I'd like to see the additional two verses from Clandillon (or from Hyde)

People are saying there is no proof that the song was sung in Ireland before the 19th century and that it may refer to the Napoleonic wars rather than the Wild Geese. Well, in Irish the song does refer to "d'imigh na géanna", the geese are gone. Admittedly a song may refer to something that happened well before the song was composed (whether we are talking about Wild Geese from Ireland or Buttermilk Hill and the American Revolution). From what I read on this discussion thread, the 19th century broadsides show that by then the song was widely disseminated in English language version in the British Isles. So it may have been sung in Irish for some time previously.

Buttermilk Hill was indeed the site of a battle in the American War of Independence according to this article about Early Pocantico History

My owm theory is that the song was brought to America by immigrants both before AND after the Irish famine, and disseminated from more than one immigrant source.