Harlow's is the only known non-revivalist version. I've never seen anything very similar to it.

Compare it to the bawdy songs in the recently published "Bawdy Songsters of the Romantic Period." These were songs performed in disreputable English saloons in the 1830s. The quasi-literary style of "The Priest and the Nuns" is similar. On the other hand, the other songs all take place in England.

Anti-Catholicism might account for the priests and the nuns, but the reference to Austria must be unique in American folksong. Why not France or Germany or Italy?

At any rate, considering the subject matter and the unusual tune, I have to believe that Harlow is printing something he really heard.