And the aesthetic of Nightmare is very similar to films made by the Mystic Knights of the Oingo Boingo, which sort of indicates that maybe Danny Elfman had a bigger influence on the art than Burton did.

I'm as big an Elfman fan as anyone - I host an Oingo Boingo podcast - but even I wouldn't go that far. I'd say that Forbidden Zone and Nightmare share some aesthetic ancestors, but the visuals are distinctly Burton's (and Rick Heinrich's). FZ was Richard Elfman's project, in any case.