JimLucas wrote: Can I really be (almost) the only one who suspects that this song (poem?) was never meant to be entirely factual,

Of course the song is not factual. How could a whale pull a boat for forty days, or even forty hours? And whales generally pulled a ship's boats, not the whole ship! It's a tall tale, and tall tales are obviously intended to entertain, and always have been. (And are prone to be misinterpreted by humorless people -- witness the tall tale of Samson: 2500+ years old, and a lot of Christians and Jews mistake it for history and fail to see that it's one of the earliest knucklehead jokes.)

But the origin of a song, and its purpose, are entirely different. And jokes tend to be better when one understands them. A joke about the Weller Brothers makes more sense at a time when people remember the Weller Brothers. And yet, a ship named the Billy of Tea wouldn't make much sense in the Weller period. So there are oddities about the origin of the song even at a very quick glance.

All by themselves, that combination of anachronisms hint that the song is a fake. But they don't prove it. Someone seeking the origin of the song (and that's the title of the thread) doesn't need to know that the song is a joke, or even to have a sense of humor; the person merely needs data. Which we are trying to find.