Shove Her Up! is a short fragment of a shanty published in Eckstorm and Smyth's Minstrelsy of Maine (1927). The caption supporting the lone verse reads:

This little song, apparently of negro origin, has been sung in Orland, ME for several generations, says Mrs. [Susie C. Young of Brewer, Maine, 1926]. Her mother, grandmother, and grandfather, Hugh Hill Carr, all used to sing it, and she thinks her grand-father may have learned it at sea. The children of the Carr family sang it when getting in wood. It seems to be a West India stevedore’s song, admirably adapted to rolling hogsheads of molasses up a gangplank and stowing them; but even a West India negro knew too much to prefer a guinea to a ten-pound note, though he might have sung this of a one-pound note.

Indeed, one finds reference to this "popular" rhyme (with one-pound note) in the English magazine Country Life (Vol. 13, 1903). "Probably this is a remnant of some topical song current at the time when there was a strong prejudice against paper money." Here there is little context but no speculation about a West Indian origin.