At least one musicologist - can't remember the name, &*^%! it - has claimed that many of the melodies used by Moore would have been impossible to play, as written, on the traditional Irish harp owing to the accidentals which put the airs into the minor, and which the traditional tuning would not have allowed. Rather than minor, the originals were presumably modal. The minor, however, was usual for "art" music of the time, which is what Moore was writing lyrics for. Someone else must know more about this than I do. (Was it Dr. Petrie who questioned the arrangements? Or P. W. Joyce? Can't recall.)
It may be that no authentic early transcription of "Arrah, Dear Eveleen" survives.