Just been rereading the articles by L G Carr Laughton in Mariner's Mirror for 1923 Vol 9 No 2. He sets out an excellent case for the slaves' shanties origin and the whole custom originating with the cotton ships coming across from the southern states post 1815 to Liverpool and then it spreading from there into the packet ships. He mentions several examples of 'Cheerly men' in use as possibly the earliet example. He also postulates there may be something more to Stevenson's 'Fifteen men on the Dead Man's Chest' it being a Caribbean island. I assume you have the references from the United services Journal for 1834 which give the account of shantying on a revenue cutter. Here 'Cheerly men' as with Dana is given as an example. The author claimed then that CM had been attached to revenue cutters 'for time out of mind', 'and sometimes the burden is not celebrated for its decency'.
Later Carr Laughton suggests the approximate order of development for the shanty being, the cotton trade as already mentioned; then the Packet service; the emigrant ships to America; the California gold rush round the Horn; the Blackwall East Indiamen; the tea clippers, and finally the Colonial clippers. he then goes on to link individual shanties with particular periods, largely according to their origins and content.
In a later article (1952) another writer puts forward an extremely strong case for the development of the word 'shantying' from the French in New Orleans, quoting 2 contemporary accounts. I can post this if required.