Not sure whether this has been done before, but how about songs that aren't in 4/4? Or not in 4/4 from top to tail (this leaping immediately to mind).
Additional kudos to whoever can handle the weirdest time signature. I was in a prog band millions of years ago that did a track - I kid you not - in 13/8. I still have nightmares.
Another idea is to cover a track by a non-Western artist, maybe from a particular continent (Africa gets my vote). Something that might well have a rock and/or roll influence but which has a very distinctive non-Western flavour.
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