A belated and (at this point) somewhat off-topic comment:

There is a scanned but not OCR'ed .pdf of The Clipper Ship "Sheila" by W.H. Angel available online, but alas it does not include music for any of the songs, just the lyrics. You've probably found that out already by now. Fascinating reading, though. (E.g. the writer explains that for the "crossing the line" ceremony, Neptune and his court marched along the deck singing "Ruben Ranzo." Lyrics for "Sally Brown" and "Stormalong" are given in the same chapter, implying to me that they were also sung as part of the festivities.) You can read the book online here: http://www.archive.org/stream/clippershipsheil00angeuoft#page/n7/mode/2up.

Also, more on topic, by chance it happens that I ordered a reprint of Terry's book (which includes the elusive Part II) from Amazon a few months ago. In case your copy has still not yet arrived, the notes for "Hilonday" are as follows:

I learned this in boyhood from the late Mr. James Runciman. I do not know in which ship he picked it up, but one of my earliest recollections is hearing him and W. E. Henley give tounge to it at the house of the latter (in the days when he lived at Shepherd's Bush-- then an outlying suburb). Henley's knowledge of the sea (like R. L. Stevenson's) was the acquired knowledge of the literary landsman, but shanties-- especially the grim ones-- had a special appeal for him, and he was fond of singing them. The sea song, 'Time for us to go', which he incorporated in the play of Admiral Guinea (calling it a 'chanty') I learnt from him in my boyhood, to a tune which I understood was his own composition. It is a good imitation of a capstan shanty, but I do not include it in this collection as it was never sung at sea; I hope one day to publish it separately.

The first half of the "solo" and the chorus in Terry's version is nearly the same as the version given in Hugill's book, but the tune is somewhat different.

Like Hugill's it is in 6/8 time, but the lyric in the second part of the "solo" for the first verse goes "Oh rise you up, my yeller gels" rather than "Rise me up my yeller, yeller gals" and Terry's tune is . . . ho boy, I'm not sure how to do this . . . here are the three relevant measures, I hope I'm transcribing this correctly in a way that maybe you can figure out:

A (quarter note) B (eighth note) C (quarter note) B (eighth note)
day.             Oh-             -                -

A (quarter note) G (eighth note) E (quarter note) D (eighth note)
rise             you             up,             my

middle C (quarter note) D (eighth note) E (quarter note) F (eighth note)
yel -                   ler             gels,             Ah

Then it goes back like the Hugill version.