I’m not 100% sure Tolkien is right for Kubrick. Maybe but I’d be concerned that he’d make it a little too ponderous and symbolic. He’d nail the spooky dark aura around the ring though. But with the Beatles? Nah no way.
Peter Jackson’s adaptation was so authentic it looked at places just like my mental imagery looked as I was reading the book. That’s a tough thing to pull off in and of itself.
Spielberg would have made it campy. Lynch would have made it surreal, might have been cool but like his Dune would be a weird cult film take. (I like Lynch’s Dune but it’s weird.)
For some reason I think Ridley Scott could have done it if he could have gotten his head out of sci fi.