Anything more specific you can say about the timing of the book more than "movie era"?
I don't think it's a secret. It's set somewhere between the fifth and sixth movies. I haven't quite settled on precisely when, but closer to the fifth movie than the sixth. (Sulu hasn't taken charge of the
Excelsior yet.)
Yeah, the year 2287 is (comparatively) pretty well-explored, between the immediately-post-TFF DC comic books, and novels like
Probe,
The Rift, and
In the Name of Honor, but 2288 and 2289 are both untouched on the prose front. I think the only major novel set during that timeframe is most of Mangels' & Martin's
Excelsior: Forged in Fire (Nov./Dec. 2289, into early January 2290, where Sulu officially takes command).
On the other hand, there's plenty of leeway between that year and 2290, and I'm glad hear that you're filling in the gaps, so to speak -- as you rightly mention, Kirk's at a very interesting point in his life, coming after the events of the last several movies (and especially the events of Dayton's novel), to say nothing of his crew. Chekov's a good choice for examination in this era -- he's been through almost as much shit and hell as Kirk and Spock by this point, and he's not getting any younger, either.
Hoping for some tasty continuity with the DC Comics runs, of course, but either way, this era is probably my favorite in
Star Trek (with early-period DS9 coming in second place), and finally having a brand-new novel set during the
Enterprise-A years is the best news I've heard in a while.