I think there is a huge chunk of over-interpretation going on here re similarities or otherwise in tunes. The fact is that hundreds, nay, thousands of poems share the same meter, so can easily be set to the same tune. Just think of songs Iike "Tramps and Hawkers" - several songs to the same tune, and again for "Star of the County Down". And conversely, there are many different tunes that share the same meter, but not the same melody, e.g. Ye Jacobites, Sam Hall, Captain Kidd: to my mind, they are not they are NOT the same tunes, nor even changed modes of the same tune: they just share something like the same rhythm.