The above link to the American Folklife Center is interesting. "Haul" the woodpile down makes more sense then "hold" the woodpile down, if sense is important to such songs:

Yankee John with his sea boots on,
Haul the woodpile down.
Yankee John with his sea boots on,
Haul the woodpile down.
Way down in Florida,
Way down in Florida,
Way down in Florida,
Haul the woodpile down.

Although it's not much of a stretch to change from "hold" to "roll."

And reference should be made to the sister shanty "Roll the Cotton Down" which shifted from the stevadors to the high seas for work on the halliards, from CHANTEYING ABOARD AMERICAN SHIPS, by Frederick Pease Harlow, © 2004, pp. 144-145:

Were ever you down in Mobile Bay?
Roll the cotton down!
A-screwing cotton all the day,
Oh, roll the cotton, roll him down.

Cheerily,
Charley Noble