Steve, I think I may have what you're looking for:

Exhibit A: Unfortunate Rake in the Traditional Tune Archive, version #1 from Ryan (1883).

Exhibit B: 'The Doctor' from Henry Adams, coll. George Gardiner 1906. This goes with a a recognizable Roud 2 text (with some interesting idiosyncracies).

The first bar is identical, and the shapes of the two tunes are sufficiently close that I would say they are clearly related, though obviously the song has half the number of bars.

Anyone agree with me?

Thanks for the Thorp text, Lighter.