Lydia Parrish published her collection in 1942 after many years of research & collecting. Here is the version she collected. Close to what's in the DT. Note that the chorus repetes. Parrish does not note where the pulls would come in but I would suspect it's a double haul or double pull shanty, each pull coming in on the word PAY, which would probably make it something similar to a quick double haul tops'l or t'gallant shanty, only used for loading logs.


    PAY ME MY MONEY DOWN

cho: Pay me, Oh pay me,
                Pay me my money down,
Oh Pay me or go to jail !
                Pay me my money down
Pay me, Oh pay me,
                Pay me my money down,
Oh Pay me or go to jail !
                Pay me my money down.


Think I heard my captain say,
                Pay me my money down,
T'morrow is my sailing day."
                Pay me my money down.

Wish't I was Mr. Coffin's son
                Pay me my money down
Sit in the house and drink good rum.
                Pay me my money down

You oweme, pay
                Pay me my money down
Pay me or go to jail
                Pay me my money down

Wish't I was Mr. Foster's son,
                Pay me my money down
I'd set on the bank an' see the work done.
                Pay me my money down

Lida Parrish says about the last verse
"Mr Foster was the "Big Boss" at the Hilton-Dodge Mill on the west side of St. Simon's & the stevedores tell me they always sang this verse when they saw him coming."

The Hilto-Doge Mill was started in 1868 & supplied much of the lumber used in the building of the Brooklin Bridge in 1878. The Mill industry's hayday on St Simon's span the years from 1874 (when the H-D Mill was finally in full production) until the industry's demise around 1910.
This song seems that, providing my sources are at all close, that the similar sounding songs may have originated elsewhere of from this one. The English deep water shanty "Pay Me The Money Down" Hugill believes to be somewhat related to this log loading shanty. Hugill states that "Miss L.A. Smith, who gives the words & music of one verse in her 'Music Of The Waters' (1888) writes that it was used at the pumps but my West Indian friend (probably Harding) said that it was used on shipboard as a halyard song". Hugill also syas that Miss Smith says that tune (Pay Me The Money Down) is a variant of "Paddle Your Own Canoe" But the 2 shanties don't share to much tune wise only in the words to the chorus.

Pay Me The Money Down

Your money young man is no object to me
                Pay me the money down
Oh money down, oh money down
                Pay me the money down.

Barry