But as I said, Jerusalem artichokes aren't really artichokes any more than Bombay Duck is duck.
Given that the songs about a costermonger, I'd say a vegetable rhyming slang origin is more likely. But how can anyone tell these things anyway?
True, it's not in this dictionary of rhyming slang. - but that doesn't mean much. Even aside from it's being on a North Amrican website (which doesn't mean much - I've got one based simgapore), the only authority I'd trust on this is me old mate John Foreman The Broadsheet King. And he's not into the Internet.