The story I'm pitching to you that would make this happen is simple. Abrams-Verse. 25th century. Borg vs. Dominion. That's it. You're surviving. Maybe the lead character is a smuggler. Maybe he's a drunk. Maybe he's the last relic of the old Federation or, better yet, Section 31. Maybe he's got a small crew, which includes, for brute force, a Nausicaan. Who knows? All he knows is what he "believes", and that's some mysterious El-Aurian who convinces him, in a very vague way, that this reality isn't the best for either of them.
What you've written here seems fine to me. A bit tricky to pull off, but hardly impossible. Potentially a very exciting tale, albeit one that will increasingly depend upon its own mythology--even more than most! But with some compelling characters and good story-telling, you've got a real good possibility here.
Personally, I wouldn't get quite so specific about which timeline is being restored. In fact, the more I think on it the more you surprise us the better I'd like it as an audience member.
In fact, this story/series idea seems to me a good one if totally separate from any idea of the "original" versus the "Abrams" timeline. That seems to me a distraction, and even putting it in those terms answers too many questions I think such a storyline should ask.
I LOVE this... I agree completely. It doesn't even need to be a "restoration" of the Prime Timeline. It can be an altering a crappy one so that the future is good. Nero's incursion could be a great time to intercept an event, but it doesn't have to be that.
The point that you made, surprising the crew and the audience in having the timeline shift being the ultimate goal would be an incredible piece of television, in My Humble Opinion. ;-)