Digital Spy managed to catch a glimpse of the extended sequence - alien civilisations! Terror attacks from Benedict Cumberbatch! Kirk loses the Enterprise! - before meeting up with Abrams's long-time producing partner Bryan Burk to talk about the sequel and heading to a galaxy far, far away with Star Wars Episode 7.
Bad Robot is notorious for keeping things under wraps - what's prompted you to reveal more about Star Trek Into Darkness?
"The thing we are perpetually going through every time we release a movie is the studio saying, 'You've gotta get material out!' We're like, 'No, hold it back!' We like the idea of keeping secrets not for any other reason than to keep the experience of going to the movies and not having seen anything before it.
"In this case, we figured that people had already seen the first nine minutes and we could show the conclusion of that sequence. We figured if we go longer it'll give people the time to get emotionally into the story and characters. You want this to be a movie that anybody can get into. It's not really a sequel, it's its own thing."
Do you keep an eye on the online reaction once you reveal a trailer or something big from the movie?
"Yes is the answer. It's funny because when we did Lost we would just gravitate towards things that people didn't like or things that were confusing. Even when talking to JJ, he will say, 'What didn't they like?' It's not looking for affirmation as much as it is seeing if people are not liking something. We feel excited about Star Trek Into Darkness, we definitely feel this is better than the last one."
What sort of challenges did IMAX and 3D present when making this movie?
"They're both challenging. IMAX is a wonderful format in the sense that it's such a crazy-clear image. So few films have shot with it. Chris Nolan did it for The Dark Knight and The Dark Knight Rises. We did it for Mission: Impossible - Ghost Protocol and I believe one of the Transformers had parts in IMAX. There's a reason so few movies shoot like this, the cameras are big, old and bulky. They're loud.
"We're doing a TV show (Person of Interest) with Chris Nolan's brother Jonah Nolan. He told us excitedly that they had destroyed one of the cameras by accident. We keep thinking that if they can destroy all the cameras, then it'll force IMAX to make better cameras!
"3D is just an interesting format, you realise the limitations of shooting with 3D cameras, you realise the laborious process it takes to finish the film. Particularly if you don't want to just slap on 3D in post and really make it an experience. It takes a tremendous amount of manpower and great artists."
It sounds like you're being quite ambitious and aggressive with the use of 3D?
"Well, Avatar was a different thing because that was a whole world being created. What we wanted is if we're going to do 3D, we want the stuff to leap off the screen and push further. We want people to leave and say, 'Well, I got my money's worth.' This film is a rollercoaster so we're really trying to push the limits."
You created a new timeline with Star Trek in 2009, will there be a lot of referencing back to the original series and movies for those fans?
"Yes, one of the things is that the movie will always be for Star Trek fans. In the process of all us five producers working together, Roberto Orci and Damon Lindelof, to a slightly lesser extent, are crazy-hardcore Trekkies. They understand the world so we had long conversations where they put things in and would be laughing hysterically. I had no clue why they were! There are tonnes of references and nods."
Given that the Gene Roddenberry series debuted in 1966 and we've just had a huge Bond 50-year anniversary celebration - has Paramount been talking to you about making a 2016 release date for the next Star Trek film?
"We're definitely talking about the next one, but we haven't talked about a release date. We don't want to wait four years, the same amount of time between the last one and this one, but it's going to be a big year to celebrate, hopefully."
So Bad Robot will still be able to balance working on both Star Trek and Star Wars?
"Yeah. Obviously they're completely different universes, they're completely different films. The only thing in common is the word 'Star', which is why we're going to do the Ringo Starr movie as well. We'll corner the market!"
Starman's due a remake?
"Yeah, Starman we're going to do, Star 80!"
Are you close to announcing any casting for Episode 7? George Lucas has said that Mark Hamill, Harrison Ford and Carrie Fisher will all be back...
"We're very new to the process. We've only been on the movie a few weeks. The script we're still working on with the writers and Kathleen Kennedy, who's a genius. It's hard for me to comment on anything. We're still figuring things out."
Star Trek Into Darkness opens in UK IMAX 3D, 3D and 2D cinemas on May 9, and May 17 in the US.
Photo gallery - 'Star Trek Into Darkness' in pictures: