Smith has PAY ME THE MONEY DOWN, with lyrics taken from Atlantic Monthly 1858. I don't know where she gets the "English comic song" idea, and the "pay me my money" seems quite in line with stevedore songs.

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Any quick, lively tune, to which you might work a fireengine, will serve for the music of a pumping song. The words vary with every fancy. "Pay me the money down" is a very favourite pumping chorus. Somehow thus the verse runs (it is known as an English comic song):—

Solo.—Your money, young man, is no object to me.
Chorus.—Pay me the money down.
Solo.—Half-a-crown's no great demand.
Chorus.—Pay me the money down.
Solo & Chorus.—Money down, money down;
             Pay me the money down.

It seems a very strange song for men so little given to avarice as sailors are. Their parting ceremony on embarking is usually to pitch their last shilling on to the wharf, to be scrambled for by the land-sharks. Nor yet does there seem much sense in it, but it serves to man and move the brakes merrily. The following tune is sometimes used for this chanty :—
PADDLE YOUR OWN CANOE. [score]
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Even though she got the lyrics from a book, did she hear this sung? Otherwise, how does she know the tune?

Then comes "Highland day and off she goes," from Atlantic Monthly.

Her RUN LET THE BULGINE RUN is original:

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RUN, LET THE BULL CHIMES RUN. [score]

This is another favourite pumping song :—

Chorus.—Run, let the bull chimes run,
Chorus.—We'll run,—
Solo.—Away to America.
Chorus.—Way aha, way aha!
Way aha, way aha!
Chorus.—We'll pump her dry and get our grog.
Solo.—Run, let the bull chimes run.
Chorus.—We'll pump her dry and away we'll go,
Solo.—Away to America!
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Once again, the solo - chorus structure anfd the notation don't quite jive.