Joe,
My own advice on this would be to treat it as a modern remake of the old song. It only has a single source and that source is questionable at best. I'm fully aware that I am very sceptical/suspicious of single source songs being claimed as traditional but that's me!

The modern, i.e. last century onwards, way of treating song classification is to be the same song 2 items should have substantial text in common. If they merely share a theme or story they are different songs. I know Child didn't always follow this system but he died before modern scholarship came in.