It seems to me that we should pluralise the topic, and talk (if we must) about the origins of shanties. There seem to be at least several, which in more recent times have become intermixed. There is no reason why shanties could not have had several origins - many other human inventions have! (How many races independently developed the bow and arrow, or the wheel?) It would not be surprising that if you were able to travel back in time to the construction of the pyramids you would not hear something clearly recognisable as a shanty. Many things simply don't get recorded by contemporary commentators because they are seen as a commonplace.
Even more important - what is the future of shanties?