The simplest solution of all would be just to ignore the "Twenty-two, sir" line in "Adonais" and assume he said 26 instead, or maybe 25 depending on where in the year it fell.
Why not assume that he didn't say anything about his age in the new film? Why pick one over the other?
Heck, there are plenty of other numbers and minor details in Trek that we simply have to ignore, like "James R. Kirk" and the timing discrepancies I mentioned in several above posts.
Right, which is why I don't see why one would need to prefer one over the other.
The age discrepancy seems to simply flow from the characters being bottle-necked into the academy at the same time. Something has to give, so the ages were fudged a little.
It's weird, because a non-Trekkie would not know or care about the ages, where a Trekkie could not help but note a discrepancy. It seems odd to make Chekov really young and thus have to make him a whiz-kid to explain his presence at the academy only to pass with the fans, when fans are bound to notice the difference anyhow (those fans who don't care about the age won't care either way; those who do will hold it to be heretical violation of canon).
Might have been better just to make Chekov a person of indiscriminate age without having to inaugurate him as a super genius. This could potentially create problems down the road. Scotty is supposed to be the engineering genius, Kirk is the tactical genius, McCoy if not a Dr. House, is at least the highest medical authority on board, Spock is the science/all-purpose genius -- with Chekov as a another super genius it could get a little crowded. Who gets the epiphany?
That question may have just gotten a little tougher. The genius factor also seems to potentially throw the Sulu-Chekov balance at the navigator/helmsman station a little off -- if Sulu isn't a genius, is he going to be a our go to fencing guy?
This isn't an insurmountable problem, but a complicating wrinkle - another thing you now have to keep track of, unless of course all reference to it is dropped in later films. In that case it just becomes a vaguely felt question "Hey, wasn't Chekov a genius in the first film? Seems like he should have some ideas here..."
It's interesting how when you move the narrative furniture around even a little bit the details quickly ramify.