My post on this disappeared. Here's a quick re-write.

1921        Terry, Richard Runciman. The Shanty Book, Part I. London: J. Curwen & Sons.

Terry said that his shanties were based in versions that he learned/collected, but that, for performance purposes, he combined or added to them.

His "Rio Grande" was learned from a "sailor uncle." I presume that was James Runciman. His version compares well to the Runciman text given up-thread, particularly with regards to the phrase "down Rio." The only other version to appear in print so far with that phrase was LA Smith's. Terry does also acknowledge that some of his texts were similar to Smiths because they both collected in Tyneside.

Verse 1 was in Alden, via Smith
Verse 2 is Davis/Tozer
Verse 3 is Smith
Verse 4 is "Spanish Ladies"
Verse 5 - unseen by me
Verse 6 is "Hame, Dearie, Hame"

Bound for the Rio Grande

1. I'll sing you a song of the fish of the sea.
Oh Rio.
I'll sing you a song of the fish of the sea
And we're bound for the Rio Grande.
Then away love, away, 'Way down Rio,
So fare ye well my pretty young gel.
For we're bound for the Rio Grande.

2. Sing good-bye to Sally, and good-bye to Sue,
And you who are listening, good-bye to you.

3. Our ship went sailing out over the Bar
And we pointed her nose for the South-er-en Star.

4. Farewell and adieu to you ladies of Spain
And we're all of us coming to see you again.

5. I said farewell to Kitty my dear,
And she waved her white hand as we passed the South Pier.

6. The oak, and the ash, and the bonny birk tree
They're all growing green in the North Countrie.