A bit of additional info here re: the "Jan Kanaganaga" in Minstrelsy of Maine (1927). The authors, Eckstorm and Smyth, say they got it from a Captain James A. Creighton of Thomston, Maine in 1925.

James A. Creighton was indeed on the sea by the 1850s (and, I'd guess, even earlier—he was born in 1821). However, he died in 1898. He could not have given the song to the authors.

There was, however, another captain of Thomaston, Maine named James E. Creighton (different middle name). His dates are July 1861-1948. He went to sea age 15, so circa 1876 or 1877.

I surmise that Eckstorm and Smyth must have gotten the captain's name wrong. If so, we may not place his memory of "Jan Kanaganaga" earlier than the late 1870s.

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I'm still working on my theory that the song has some relationship to "Old Aunt Jemima." The latter's composition is attributed to minstrel performer Joe Lang, who began his stage career in 1870 and, a publication--which I have not seen--indicates "Aunt Jemima" came out in 1873. I have documentation that shows the song was already popular in 1873, in any case. It went through various adaptations over the years. No smoking gun to connect "Jemima" and "Kanaka" songs though. I suspect only musicologists will feel most compelled by my tentative argument about the melodic correspondence (2020 post, above).
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Perhaps I haven't mentioned this before: There's a recording of Stan Hugill singing "John Kanaka" at the first Mystic Seaport Sea Music Festival in 1980. (Were revival folks singing the song before that, and how?) Anyway, Hugill sang the song with an "odd" rhythm—it was syncopated somehow, and different than the way I've always heard people sing it. What was the exact rhythm? Well... I didn't quite note it down. But I think everyone would be surprised if they heard it.
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Here are my more-or-less accurate notes of what Hugill said about "John Kanaka" in 1980:

“Now, I have met, of course, many shantymen. Otherwise my book would never have been published. My greatest friend—and if there’s any colored people here, don’t take umbrage at this, because this is what he called himself—he was black as your hat; he was big, powerful man on the fore-hand of any brace or topsail halyard; you would never have had “John Kanaka” (if it weren’t) for this fellow—and me. If he hadn’t given it to me, or I’d have died, there’d be no “John Kanaka”; and lots of other things, but still, that’s one of them. His yelp… [] But we always called it a hitch. You couldn’t sing a shanty without making this horrible noise, somewhere or another—a cross between a yodel and a brown bear in pain or something. […] Mind you, Germans were good at it; so were Scandinavians. Of course, the Negro was best; the West Indian black man was the best. The Englishman was the most anemic—we were really hopeless at it, nothing like as good as them. Now this was Harding “the Barbadian Barbarian”—that’s what he called himself.”