I was in occasional touch with Wes Craven back when he was preparing to do a sequel to the original HILLS HAVE EYES. He wondered what the title should be, didn't like just HILLS HAVE EYES 2 (though, of course, that's what it ended up as). He didn't think too much of my THE HILLS HAVE TWO EYES, but was amused by my wife's suggestion of THE HILLS HAVE NOSES.

The quickest original/remake turnaround I'm aware of is GET CARTER being remade a year later as HIT MAN. Another fast turnaround was THE FALCON TAKES OVER being remade two years later as MURDER, MY SWEET. Of course, that's more a matter of another version than an actual remake.