John, your ex. from 1836 may explain why Dana deleted "Grog Time a Day" from his list of titles. It may have been the same as the song he called "Captain gone ashore"!

Given the date, one can probably assume that "Fiferail's" is the song Dana heard. If so, it doesn't seem to have been a one-line, one-pull shanty. I suppose it would have belonged to capstan work.