The 'North Atlantic Squadron' MIDI is the tune for both verse and chorus of that song, and is pretty much the same as the chorus for 'Away with Rum'.

Joe's contention that the song must come from the "North Atlantic Squadron" series of songs has a fair amount going for it; it wouldn't be the first song with different tunes for the verse and chorus where the tune for the chorus became subsequently attached to a later song.

1963/4 seems to be the earliest date anyone on this thread has yet put to 'Away with Rum' under its various names. The earliest date I can remember singing it (I picked it up aurally rather than from texts) was in the early 60s ('61-'64) during parties at Melbourne Uni. While is had only about seven verses (at that time and in that place) it rapidly acquired extra home-grown verses that melded with other versions at universities around Oz. But the temperance organisation in the chorus in Oz (within my hearing) was always the Salvation Army.

But I can't yet shed any light on earlier transformations/origins.

Cheers, Rowan