My best idea (so far) is that the third JJ film restores the "Prime" timeline, making a prelude to a new series.
I wouldn't be surprised if that's what happens. It does seem like there's some philosophy afoot that 'timelines want to repair themselves" and once the movies are over after the third (?), the original need for providing a free and clear playground will be gone, because those characters are not going to be played by those actors in any TV series unless it's animated and they can be played by voice-alikes.
That way the third movie could end with some kind of "re-emergence" of the "correct" timeline and provide a link to a TV show timed to coincide with the third movie (and announced after the upcoming one definitively proves the franchise's viability by being another big hit).
If it's live-action, the characters will be different, so the problem that "we've already seen these stories" will be gone. But if the TV series is animated, the Abrams characters can be used, and then re-merging the timelines has a lot less value.
.
Using a portion of the third Star Trek movie under Abrams to set up a new series would be a good idea.
Such as: Introduce at least one new character who will become the lead of the TV series, or the Spock-type "alien other" character who is always such a major draw. That will help alleviate the main problem (other than budget) of a live-action series, that the characters have no name recognition.
Whatever the new series turns out to be, I can guarantee you that it will not be set in the old continuity, will not take place after Voyager, will not have cameos of old characters. In other words, it will not be more of the same stuff that people got tired of the last time.
The issue of people being tired isn't an issue anymore. The people who got tired of the UPN series are not the same people as would be watching a new series, or even the same people who are watching Abrams' movies. The audience for a new series won't necessarily even know that there are two realities in play, or be able to tell what continuity is being followed, unless the third movie comes out and tells us what's happening - such as by having a character state, "ta dah! the timelines have now re-merged!" Which to the average audience member will just be meaningless technobabble anyway. Only the core fans will care/argue over that issue.
Cameos of old characters are perfectly possible, if whoever is making the show (most likely Orci) decides that's an interesting idea. Considering the age of the TOS actors, and that many have passed away, the roles would more likely be recast. Another element that fans will appreciate more than new viewers.
But post-VOY does seem unlikely. Why leave the 23rd C when it's been working so well? (Other than the inevitable time travel episodes of course. Which could involve characters from the other series, played by the original actors or recast.)