Tim, I believe the simple answer is, "They are all similar."

Verbose, opinionated answer: I consider it to be all one tune, "THE" tune, where the differences between performances aren't significant enough to say "Ah, that's a different tune." I don't actually think there's really such a thing as "versions" of chanties. (For the most part. There are probably exceptional cases that aren't coming to mind.) Because that "certain degree of variability" is built in, on the one hand, and on the other hand you need "the" tune to anchor you; the tune itself "is" the chanty. (Whereas, as an example of contrast, the narrative text "is" a ballad, and when you see either the narrative going in divergent directions OR the text is set to clearly different tune, we begin to talk of "versions.") So it all comes down to what degree of difference one thinks is significant. If I say "water" and you say "water," there *is* a difference in sound. But for most situations we're concerned with, they are the "same"; it's only in some arcane context (like a linguist mapping regional phonology) that their difference is significant.

(Yes! I did just write a whole paragraph basically stating the obvious. Good thing Mudcat doesn't charge me by the word.)
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Here are the texts mentioned so far, I think, that have information about tune. I can have a look at each of them later.

Gordon (This is a recording. I transcribed the lyrics from the recording at LoC. Looking in my notes, however, I see that I wrote down the tune for other songs I listened to at that time, but didn't do it for this. Which tells me I didn't think the tune was notably different from the most popular way people now sing Reuben Ranzo).

Noble Brown

Gardiner

Linscott

Adams - I remember that the second half stands out a bit. Subjectively and without strong argument as to why, I think something sounds "older" or more "authentic" about it and I like to sing it.

Whall

Bullen

Davis and Tozer

Masefield

LA Smith

Alden

Dick Maitland

Tayleur

Rutzebeck- I don't have this. Is there a tune?

Robinson

Walton

Hugill