The similarities between the song and the "dying declaration" appear to be too generic to show a real connection.

Not just my opinion - but I can't recall who first pointed it out. Horace Beck?

In any case, Beck did argue that the song came from not one but *two* "lost" broadsides. Which is probably at least twice as unlikely as coming from either one lost broadside or from the Fernandez leaflet more than 50 years before the song's first known appearance.