My source has 1818 as the date of first German publication which is so close to Joe's 1816 that we shouldn't bother about that any longer, but:

Was the tune really ever the basis for a sea song or has someone once misread 'Sicilian Marian song' for 'Sicilian mariner song' (or was there even a typo like 'Sicilian Marina song'?)? Of course my hypothesis doesn't exclude the possibility that mariners at times of trouble did actually sing a Marian song.

Wolfgang