Thanks, Joe, for transcribing the notes from the Boarding Party's CD. I became interested in this song after seeing it on-line in "Naval Songs: A Collection of Original, Selected and Traditional Sea Songs," 1883, no author given. Its on Google Books, and is a treasure trove of shanties and songs from a period where they would have been much more current than later compilations.

Anyway, in "Naval Songs," this ballad is given as "The Constellation and the Insurgente," with another (greatly inferior, IMHO) song entirely appearing as "Truxtun's Victory." The tune is also given, which does not correspond with the one used by The Boarding Party -- a fact which puzzled me until I found this thread. The tune given in "Naval Songs," to my ear, sounds vaguely like The Watersons' "Warlike Seamen," which is how I'll probably end up doing it.