Toward the top of this thread, Joe Offer and others note that the "Gambolier" melody was first used on stage in 1873; and that Fuld's Book of World-Famous Music adds:

> "The words (of Dunderbeck) appeared in Our Own Boys Songster (New
> York, NY, 1876), p. 6, under the title "Dunderbeck's Machine," to the
> "Air-Thomas's Machine." "Dunderbeck's Machine" is there said to be
> "By Ed. Harrigan," but this might also mean "sung by" Ed. Harrigan...

Nobody on this thread seems to have looked up "Air-Thomas's Machine." There is no song by this name that I can find—but there *is* an *air* called "Thomas's Machine"! It reportedly dates from 1873:

http://monologues.co.uk/musichall/Songs-T/Thomas-Machine.htm

And here is an Amazon link for sheet music that seems to back up that date:

http://www.amazon.co.uk/Thomass-Sewing-Machine-Song-begins/dp/B0000CZ0EM

If the date is correct, then this predates Dunderbeck and is the first song to link the "Gondolier" melody to verses about a machine. The subject matter is less unusual than Dunderbeck, so it's easy to imagine Dunderbeck as Harrigan's deliberate attempt to make the "Thomas" lyrics crazier.