Rhyme consistency isn't a good indicator of antecedence--later versions often clean up sloppy rhymes in original doggerel.

It turns out that the differences in wording between your text and the broadside are actually few, so I want to apologize for what may seem like quibbling. I suppose one reason the transcription struck me as so very different was the wholesale omission of nearly all the original punctuation, explained by having retrofitted the similarly deficient Ninepenny Marl text.