TOS works in movies to a degree. TNG really doesn't. What they need is something that works for them. Completely. So it has to be something besides those two. Turn it into a star vehicle like the Mission: Impossible movies did, and then you have a Star Trek film series that's completely native to the films. The Abrams Trilogy was part of the way there, but not all of the way there.
You can keep Kirk, keep Spock, have everyone else be new characters, and no one who doesn't follow Star Trek will know the difference. Make it a Keanu Reeves movie first (just as an example) and a Star Trek movie second, and those people will be thinking of it as going to a Keanu Reeves movie that just happens to be Star Trek. A Tarantino-directed Trek movie would've been a similar idea: a Tarantino movie first, a Star Trek movie second.
The trick is they'd have to bank on the right movie star.
A Strange New Worlds film actually wouldn't be too too far from this. Anson Mount as Pike. Pike would effectively be like Kirk to John Q Public. Spock is Spock. And then everyone else, to them, would be totally new characters. If Anson Mount were a bigger name, and it wasn't called the "Prime Timeline", SNW would actually fit what I suggested above perfectly. Except, once they'd have cinematic success, why would they go back to making SNW as a TV series? So I think, for that reason, an SNW film wouldn't happen.