New Zealand is another interesting one. Our demonym is "Kiwi" from the bird. I guess technically it's "New Zealander", but I don't think I've ever heard someone use that.
Would it be possible that perhaps the demonym is the name of the people, a noun, while the adjective is another thing, that can happen to coincide with either the place name or the demonym or something else, on a case by case basis?