cnd,

That's plausible, thanks!

The criticism that I have is that you seem to have set the meter then molded the melody to fit it, as if the melody constantly follows a long-short rhythm. Yet it doesn't do that. If it did, I think the song's meter would have been readily inferred consistently and "correctly" by all listeners. I guess where I'm coming from is not trying to imagine how we could fit the lyrics and pitch sequence of the melody to a windlass but rather to deduce how the historical actors did it.

Moreover -- not a criticism, but a counter point -- it makes what feel like very strong points in the verse meter fall on the second beat, rather than the first/downbeat of measures. Specifically, "a-WAY" and "rolling RIV-er". The data from other chanties tells us that "a-WAY" usually sets up a big extortion on "WAY". "WAY" and "RIV", besides feeling intuitively to me like they need to be on these "downbeats," can be seen placed there when the whalers row to the song.

Alden - the source I keep referencing -- has his two versions in 6/8, too! (Well, actually, he has the first in 6/8 and the second, inexplicably, in 12/8. But same thing, right?)
Alden transcriptions
These two are the first in my recorded example:
https://youtu.be/V_CnZytGXUI
So here we have the 6/8 that you've helpfully suggested, Carter, but retaining the timing (some long notes, bunches of short notes) with which we're familiar.
Now: When I sang it, I "converted" the 6/8 to 3/4 because I could not get the hang of tapping out the beat to 6/8 while singing that rhythm! Feeling the 6/8 against this rhythm is like trying to perform a West African polyrhythm! I figured that since nothing is heard indicating where the pulse is per se, my "thinking in 3/4" while performing it wouldn't make much difference (correct me if I'm wrong). Alden's rendering in 6/8 also preserves the emphasis of purring "-WAY" and "RIV-" at strong structural points.

you / SHAN-andore (-) i / LONG to hear YOU,
hur- / RAH, YOU rolling / RIV-er (-)

This is why I have been emphasizing Alden so much. It makes the most sense *to me*. If we know the song is supposed to work to this "6/8" then everything is peachy. Folks hearing that without 6/8 time being beaten out (or "shown" through the action of the windlass), however, would likely be confused and unable to infer the singer's internalized meter.

Comparing the West African music again: In one of my classes, I always play (one of) the familiar West African bell patterns without any other points of reference and all the students clap (to show the beat) in a way to suggest 6/4 instead of 12/8.
https://youtu.be/twvlle4abt4
Then, when I throw in the pulse (where the guy is tapping his foot in the video), the students kind of fall apart.