Hi, Brian. I don't see a great deal of similarity between the Harrigan-Braham melody and that of the Dorset singer, except in the final phrases.

It seems likely that Harrigan or Braham was familiar with a line or two of the earlier song and was inspired to write a new song around it. Any general similarities between the two melodies results from the influence of the final phrases on the new composition. The mention of China in both songs may or may not be coincidental.

But even if H or B knew the entire broadside, the their own song remains an essentially different production with a distinct subject and an entirely new refrain. No one could confuse the two pieces, and no amount of unconscious or hit-or-miss "folk processing" could evolve the one from the other. They aren't "versions" of each other any more than "Rock around the Clock" is a "version" of "Roll Me over in the clover."

I don't see the broadside as a "template," which is a mold or a pattern on which variations can be imposed. While the H-B song is not 100% independent, its connection with the broadside song is visibly minimal.