Brian,Hal an Tow is certainly a Cornish song. A children's ritual accompanied by the song is still performed in Helston during May.
I'm not sure where your 'missing' stanzas are from. Every version I know is fairly close to the DT one. I'd be interested to know where you've heard extra verses.
As far as 'Aunt Mary Moses' is concerned, I'd assume that this is simply a misheard interpretation that has over time been passed into tradition and hence corrupted the original meaning.
The Watersons sing: 'God bless the merry Moses'
I think that overall, it's one of those songs that is impossible to come to any reasonable conclusions about.
Peter Kennedy, for example, mentions three totally different theories as to what the title might mean.
Ed