I agree with everything you said, PoppaG! When I said a cover of Archibald's version, it's just that Archibald's was the first recording I knew of. As you say, the New Orleans version is a traditional song in its own right.

And there's a third stack-o-lee/stagger lee also, which is the "toast" or spoken-word version, an entirely different set of words with lots of graphic sex and violence. This has been set to music by Johnny Otis, Nick Cave and others.