The problem for Brian was his main role within the group was more or less obsolete by 1967. Since the Beatles had achieved their early success, his principle role if I'm remembering things correctly and as Rjrrzube notes, had to do with touring and there was no way they were going to go on any sort of tour after 1966. By the time he died Brian's principle role was essentially negotiating the egos of everyone involved in the group. My guess if he lives is that he'll probably be the one running the Magical Mystery Tour idea, or at the very least putting his efforts into insuring that it isn't the total disaster it was IOTL. He might even hire a real director for the project. I also think its possible he might have gone to see the Maharishi with the rest of the group. After that, he'd be putting all his efforts into keeping the group together. He'd also probably try to find a film to fulfill the contract with. His survival would had an emotional impact on all the members of the group, especially John Lennon. (Don't worry I'm not trusting Goldman's bizarre theory here. I'm just saying that since Lennon had lost his mother, and lost his best friend, he probably took Brian's death a bit harder than the rest of the group. It's more or less a guess on my part. )
As far as the film is concerned, the best idea I can think of is something like a one off concert filmed in a studio. Let it Be as we know it would never happen. I can't see Brian supporting the idea of having the band come in very early to record music while on camera, in the midst of a period when the band was bickering and had begun to lose the cohesiveness that had defined it in earlier years. His goal would have been to keep them together at any cost. The only problem with the studio concert idea is that it might have been a bit too similar to "Rock and Roll Circus" in some respects.
I'm not sure if his efforts save the group in the long term. Though the breaking point might come later than it did IOTL. It might even be George Harrison, not John Lennon who becomes the first of the group to depart on a permanent basis. (Harrison and Starkey quit before Lennon did, but they were obviously convinced to come back.)