This is probably a long shot, but see what you think. I did a Google search on "Heave to the girls" and found a couple of interesting things. First of all there was this from William Clark Russell's book MAROONED (1898):

http://books.google.com/books?id=tAsXAAAAYAAJ&pg=PA19&lpg=PA19&dq=%22Heave+,+to+the+girls%22&source=bl&ots=-Ojmc7t-TC&sig=XrcEcK

Granted this is not a shanty, but about a mate calling for a shanty. But then there is this from A SHIP OF SOLACE, by Eleanor Mordaunt (1911). Look at the fourth verse:

http://www.archive.org/stream/ashipsolace00mordgoog#page/n310/mode/2up

And there is this from John Ward's web page, which he says is from Frank Shay's IRON MEN AND WOODEN SHIPS. However, this is not what I find in Shay so I'm not sure where it is from. Again, check the fourth verse:

http://www.jsward.com/shanty/rio/away_rio.html

In at least two versions of "Rio Grande" there is a verse that has the line "heave to the girls" or "heave to the maidens". I have not found any other instances of this in other versions of "Rio Grande" but I haven't checked that many. I suppose that if Dana was referring to this shanty he would have called it by the name of "Rio Grande" but it is an intriguing coincidence.