Thanks for the help, guys. Interesting to hear about those broadsheets. I imagine they'd just say "Sing to the air of Cheer, Boys, Cheer" (i.e. by Russell). Hugill may very well have been the only person to document a melody for the unique, chantey adaptation of the theme.
It's interesting to read what Masefield wrote "Sebastopol." I am quoting from a web page, here.
One of the best, and most popular, capstan chanties is that known as "Sebastopol." The words are, if anything, rather better than most. The tune is excellent and stirring. It moves to quicker time than most capstan chanties.
(The version of Masefield I have, which appears to be a 1908 second edition, does not have this passage.)
Anyway, surprising that it was "most popular," yet we are hard pressed to locate one now!
I am going to try out recording a version of it, within the next few days, to see what the tune "feels like" in practice. One thing I am puzzled by is why, with such an adamant rhythm to the phrase "cheer, boys, cheer" --all driving downbeats-- the chantey version would have a dotted rhythm there. Seems weak.