I love the song, don't know much about it, your interpretation of feather goose was an eye opener to me but it makes sense, I had always wondered about that verse. The recording I have of it, by a local band called Tenpenny, has the following verse which is not in the DT version:

John the Bum(?) went marching on
'Til he met with Sally Dover
He kissed her once, he kissed her twice
He kissed her three times over

The chorus makes me think this might be a seafaring song - Hal (as in halyard) and tow being synonyms for hauling or pulling on a rope (something sailors used to do a lot of) and if you spell the second line "Jolly rum below"...well you get the idea. Thoughts?