^Lots of onscreen evidence contradicts other onscreen evidence. Sometimes you can reconcile it, but sometimes it's just too much trouble for too little gain, and stardates are definitely such a case.
And sure, Abrams's scheme is the only one that has any real chronological coherence to it, but it's problematical in other ways. As I said, why even call them stardates when they're really just Gregorian calendar dates expressed in a slightly different format? Although I can see why they did it. The movies are designed to be accessible to a new audience, viewers who aren't already familiar with the universe, so just using years for stardates is a handy, quick way to let the audience know that the first movie began in 2233 and took place mainly in 2258 and that the older version of that guy with the pointy ears came back in time from 2387. So from that standpoint I can see the practicality of it. But in-universe it's harder to justify.
Anyway, I long ago decided that pretty much any and all numbers in Trek are best taken with a grain of salt. Different creators make different assumptions about various numbered phenomena like dates and distances and ship registries and so forth, or they don't much care about the specific numbers since they're more concerned with plot and character (as they rightly should be), so it's hard to find any real consistency in any numbered property of the universe. So I try not to take them too literally, and often I just ignore them.