Lighter,

My interpretation is based on inferences drawn from the text references and on the text of the chantey, as well as many hunches based on what I think I understand about the genre. Not much to go on, but something to consider.

I'm pasting some of the sketchy notes on historiography here, from my YouTube vid.

Being [ostensibly] a song of the translatlantic packet ships (1840s-50s),[perhaps these dates are really too early] as per oral accounts retold in later days, "Blow the Man Down" *appears* to have existed since those days. However, in the textual record, so far as I am able to tell at present, "Knock a Man Down" actually appears first.

Adams, in his 1879 ON BOARD THE ROCKET, describes some of the chanteys he heard circa 1850s. It is one of the first books to present chanteys WITH musical notation (albeit with some irregularities). Among them is "Knock a Man Down," but NOT "Blow the Man Down." ...Adams noted just the first [verse], but he goes on to say that on that pattern, one "can wish he was in every known port in the world, to whose name he can find a rhyme." ... So, here is THE classic chantey lyric paradigm, that goes back to the earliest documented samples of chanteys' predecessors, the cotton-stowing songs of Mobile Bay. And, accordingly, the first verse here is about that. So, "Knock a man Down" has the earmarks of an African-American "chant" from the early days. [in the verse style/content] [interpretation]

Adam's notation of this chantey was reproduced, fixed up, in Luce's 1883 collection NAVAL SONGS. Elsewhere in that collection, Luce also includes an item called "BLACK BALL. 'Chanty' Song. Sung in the merchant service in heavy-hauling." Funny, he makes no comparison between the two songs. Perhaps this was because the melody of the latter was quite a bit curvier and had a completely different text -- the "Black Ball Line" theme. ...

What this shows is that, at that time, "Blow the Man Down" was certainly not a "famous" one in the contemporary sense. However, in LA Smith's book from 1888, she does mention "Blow the Man Down" by name, just not with a big hullabaloo.

Back to "Knock a Man Down" -- it appears again in 1914 in Cecil Sharp's chantey collection. He got it from John Short. ...

I find the "blow the man down" chorus with the common lyric variations of that chantey to be incongruous, inspiring me to believe that BTMD is the result of grafting some text upon a previously existing form.

So that's part of it. It's hard to lay out the musical analysis and hunch-y parts of it.

On the other hand, I don't see any proof that KAMD and BTMD are variants and which would make my interpretation wrong.