Thanks so much for adding your notes directly to this thread.
Captain Hathorn may have added his own interpretation to the expression as heard at a minstrel show or in discussions of minstrel shows with friends. I've been thinking that the idea of dancing down a chalk line as if carefully balancing a pail of water on your head may also play a role. When a ship is really tearing along with a brisk wind, to achieve top speed everything has to be perfectly balanced: the setting of the sails, proximity to the wind, stowing of the cargo, all variables.
I think this expression is now aqppropriately nailed and will pass the information on to Catherine Petroski who based a book on Susan Hathorn's diary, which was the basis for my song. Catherine has been wondering about this odd expression for years.