And many thanks for your further help. I didn't have the date of William's funeral, so many thank you for that.
You have the right family, although the 1813 Robert was buried a few weeks later - on 5 December. So, as with their son James, the name Robert was re-used some years after the first child to bear the name passed-away.
There are three more children to this marriage for whom I have yet to find a baptism record: Joseph (1818-1885); Ann (1826-1890) and of course Robert II. I am also fairly certain that Henry died in infancy but have no proof as yet.
Thank you for the link to the newspaper archives - I will have a bit of a browse.
I really think I need an eureka moment for this one, if I am ever to get to the bottom of it. Any further thoughts, gratefully received.