Apparently, "...Old Maui" was in Gale Huntington's Songs the Whalemen Sang, and it says the song was taken from the 1958 log of the ship Atkins Adams out of New Bedford. Earlier, it was in Colcord (1938). More here, at contemplator.com

The phrase occurs often enough, I've never thought about it too much, and just assumed it meant "get the hell out of Dodge".