Beginning of a more detailed chronology on this.... I am curious as to where certain 'myths' about this song may have started in the 20th century literature and in the revivals.

The following text is supposed to have been located in a journal kept at sea in the 1860s by Capt. James A. Delap of Nova Scotia. It's the earliest that I can recall seeing. Presented in:

1951        Doerflinger, William Main. _Shantymen and Shantyboys: Songs of the Sailor and Lumberman_. Macmillan: New York.

A bully ship and bully crew,
      Lowlands, lowlands, hurrah, my John,
And a bully mate to put us through,
      My dollar and a half a day.

I wish I was in Liverpool,
With the Liverpool girls I would slip round.

Oh, heave her up and away we'll go
Oh, heave her up from down below.

Oh, a dollar and a half is a shellback's pay,
But a dollar and a half is pretty good pay.

Oh, rise, old woman, and let us in,
For the night is cold and I want some gin.

I don't know the story behind this journal. I presume Doerflinger saw it as part of his fieldwork in Nova Scotia in the 1930s and 40s (?).

Right out the gate -- assuming this is authentic -- one can see the "dollar and a half" chorus.