I realize it would be just as heretical as J.J. for some people, BTW, but I'd be REALLY intrigued by a Richard Kelly Star Trek.
He has a habit of using real science fairly accurately in places but making it incomprehensibly woven it with weird fantasy elements. I think that could be interesting for Trek because he could really sell the future aspect by making everyone feel like they didn't understand a lick of what they just saw and they weren't supposed to either.
He did Donnie Darko, Southland Tales, The Box. I don't think his prior work is perfect as credentials go but I kinda like the idea of a director doing a type of film he hasn't done before. He's good at working with actors and a range of camera techniques, including explosions and SFX. I think the real trick is pairing him with commercial writers who ground him, kinda like how Mark Frost grounded David Lynch on Twin Peaks.
(It's actually a pretty common pairing in Hollywood. You get an almost borderline schizophrenic artist who makes incomprehensibly dense high art and someone who thinks like a merchandising/advertising exec and force them to collaborate and if they don't kill eachother, the result is almost always great. And REALLY great writers generally can play both roles, reining themselves in.)
I'll also add, this pairing is pretty much what gave us Ghostbusters. Dan Aykroyd has pronounced, I believe diagnosed Asperger's (he identifies publicly as having it) and is very fixated on time travel, UFOs, and the paranormal. And his screenplays are unfilmable, densely packed. I seem to recall that his concept for Ghostbusters had them on a space station and revealed that ghosts were artifacts of time travel and the rate of the universe's expansion creating spatial folds or something like that. And the humor was VERY highbrow. Like, you'd need a Ph.D to get most of it. But pair him up with Harold Ramis and you wind up with Ghostbusters, which is more commercial than anything Aykroyd could do on his own but still, well... I think it stands out as being tremendously more cerebral than Ramis' work on Meatballs or Caddyshack. And Ramis paired with pretty clever writers for Analyze This and Groundhog's Day.
Aykroyd brings the genius, Ramis made it filmable.