The Yosemite scenes in TFF suggest a late Summer/early Fall placement.
Uhh, global warming!
Accepting that TWOK begins in late March, and TSFS begins a week or two later, in early April, then TVH takes place around July. So the shakedown cruise couldn't have lasted six months, as that would place TFF around January, too early for the season portrayed in the film. I'd place TFF about two months after TVH.
I have about 3 weeks between TWOK and TSFS. There had to be time for the damaged ship to limp home, for Carol to leave, for Saavik to formally graduate from the Academy (her department color went from cadet red to command white), for injuries to heal, and so forth. It's odd that Spock hasn't matured more in that time, but his growth did seem to be accelerating exponentially, so it would've started out slow.
So that puts TSFS about halfway through April, and I assume it takes close to a week. TVH is three months later, which is late July; but we don't know how much time passed between their return with the whales, their trial, and their assignment to the E-A. Actually that could've taken months right there. Although in order to be consistent with The Genesis Wave, Book One
Ch. 14 (the "Genesis Report" chapter Dave Mack wrote), I have it as about two weeks, putting the end of TVH in early August. The frame story of To Reign in Hell
goes next, and says that the E-A is in spacedock being readied for final testing and flight. I figure that could add a few weeks before the shakedown starts, so I have the shakedown being September through February. Afterward, according to TFF, Kirk gave Scotty three weeks to repair the ship while the crew was on leave. So that moves the start of TFF into mid-March. Not sure if that fits the Yosemite scenes, but it's closer than January.