It could be possible that it was recited rather than sung (unless there is reference to singing in Eckstorm's notes) and thus maybe there is no tune. I tried to find this in the roud index with no success. One place you might consider looking (if you haven't already) is in the "Old Favourites" column of the Family Herald, although I don't think they printed that many tunes. But at least you might be able to get more information about the verse. There's also always the possibility that Franz Blanchard took it from print and made up the story about the Newfoundland seal hunter.