It is possible PP&M got this song from an intermediary source, rather than mangling the Irish they couldn't pronounce. (I can't either, which is why I sing "Gone the Rainbow/Buttermilk Hill" along with Irish traditional songs: better the specificly American version than mess up a lovely thing in Gaelic.) I found a version in Pete Seeger's Clearwater Songbook that was from the lower Hudson Valley, sung by the Allison family, with same first and last verse, no chorus, and a middle verse running:
Me, oh my, I loved him so,
Broke my heart to see him go
Only time will heal my woe.
Johnny's gone for a soldier.

The verse fits neatly into the PP&M version, so I sing it, too. I do believe that it started out as an Irish Gaelic song, and went through several adaptations (including mangling the English words for weaving tools up for sale) before slipping into the PP&M repertoire.

Joanne in Cleveland, with no aspirations whatsoever to sing in Gaelic of any flavor.