Fascinating thread, but there is one possible origin which has never been mentioned. The red coats of soldiers have been alluded to, but might it, in fact, refer to the red coats of the Royal Marines. Every R.N. vessel from a frigate upwards carried a complement of Marines. Not normally involved in the working of the ship, in some circumstances the marines would be expected to add their weight to hauling and, less adept at such duties, would become the object of guarded ribaldry from the Naval crew, exhorting the "blood red roses" to hang down.
This, of course, is only conjecture, particularly as the Royal (sailing) Navy did not officially allow work songs. Nevertheless, naval vessels on distant, detached service would often press extra hands from merchant ships and whaling vessels, despite any (sometimes dubious) letters of protection. These hands might bring songs with them and would, on discharge revert to their former merchant occupations, taking adaptations of the songs with them. And so it goes on!!