Dave: “So it seems to be pretty certain to me that the Sloop John B (both the boat and the song named after it) was named after its captain, John Bethel, who lived in the mid-to-late 19th century; and that the song dates from around that time.”

"The real estate agent told me..."? The 'source' that convinced the current homeowner, and you, was social media. Even then, not as well sourced as the thread you are posting in now.

fwiw: The salesperson's patter is lifted straight from the McCutcheon fable. The Bahamian process is little different from the hundred-and-eleventeen “Washington Slept Here” roadsides all over New England.

A copy, or even a retrievable reference to, a poem or a song that actually predates Prouty/Le Gallienne oth would be interesting to say the least.