I don't follow your reasoning here.
No wonder, as there's none - it's of course 2265-66, not 2266 only. Sorree!
(Although I did read MMoMiM's comment as "Timo's Reasoning (TM)", which would be par for the course, I guess...

)
Indeed. And let's not forget TAS, either. Or the question of how long Kirk was in command before the FYM, and when exactly WMNHGB happened.
But the thing is, nothing AFAWK defines the five-year mission
except Kirk being in command. The mission doesn't start at any specific achievement or mark. And while the mission is ongoing, nothing defines it: the ship may be out in uncharted space, shuttling stuff in known space, visiting starbases, visiting Earth, whatever.
Kirk is very much in command in the second pilot already (even if his rank still remains that of Commander, as per sleeve braid). So there's no demarcation line between the second pilot and the series episodes.
Our only alternate hope would seem to be claiming that the five years are bookended by something happening to the ship - a long layover ending in the start, and a long layover following the end. We know there's a layover after the end, but not even "Q2" tells us that it would be
immediately after the end. And we know nothing much of the beginning.
Also, when the parallel timeline of ST:ID introduces the five-year deep space mission as an all-new invention, it seems to be all about a set of people packing themselves aboard, sailing out, and returning five years later. ST:B reinforces that idea. But TOS didn't work like that: there was crew rotation galore.
Here, I completely disagree. TOS-era stardates obviously bear no resemblance to TNG-era stardates, and trying to arrange TOS episodes by stardate order makes an utter mess of things. Plus, just on general principle, I try to avoid drawing conclusions about TOS continuity based on things established in later series (unless they're completely unequivocal, like the remark about 2270).
But "trying to arrange" is very, very helpful if you bother to do it. TOS instantly becomes the five-year mission; Kang's remarks about the passage of time in "Day of the Dove" suddenly make sense; Chekov gets aboard before "Space Seed"; Kirk doesn't shuttle back and forth to SB11 within two weeks, with amnesia in between; etc. etc.
There's no real downside, either. The only case of overlap could be chalked out as a slip of the tongue by the fatigued Kirk, dictating a slightly too high stardate towards the end of his "Miri" ordeal by swapping the last two digits.
But we do, in fact, have other evidence. We know "Charlie X" (early S1) happened concurrently with Thanksgiving on Earth. We know "The Deadly Years" (mid S2) happened when Kirk was 34 — i.e., if we accept his canonical birthday, sometime between March 2267 and March 2268. We know "Day of the Dove" (late S3) actually happened three years after "Errand of Mercy" (late S1), not just two. And so on and so forth. We don't have references to specific years on the Earth calendar, but it's still possible to do a fair bit of logical interpolating.
Certainly. And slotting the episodes to years 1-5 as per the first digit of their stardate works pretty well there.
FWIW, in my headcanon, S1 spans mid-late '65 to late '66, S2 spans late '66 thru '67, S3 spans the beginning of '68 thru early '69, and TAS takes us to the end of '69. (As much as possible, I also try to allow space for a lot of the novels in there, but of necessity canon comes first.)
The stardates hop forward a lot during the first season and a half. Allowing this to represent more passage of time than the second half of TOS is IMHO a very workable interpretation. Heck, one could slot the TAS episodes in there by their stardates, too (Chekov and Arex might simply take alternating leaves). Or put the TAS episodes beginning with 1 at the next "stardate decade", just like the DSC episodes appear to represent the previous "decade", with the decade digit omitted.
All of which is a long digression by way of saying there's no particular reason (in or out of the OkudaChron) to place "Obsession" in 2268 rather than '67, which means the cloud-creature attack on the Farragut should be at some point in '56, already in the past vis-a-vis Discovery.
And since it's "eleven years" very specifically, there's little point in trying to say it's "actually just ten". McCoy wouldn't be counting the multiples of 365 days (or multiples of 1000 stardates) - he'd glance at Kirk's records, see that the
Farragut one falls on a year that's the current year minus 11, and use that. Heck, he might even do the usual thing and fumble the calculation, in fact referring to something that happened 12 years earlier!
Still lots of room for ambiguity there, though. We don't know how many years separate Jim and Gary (as little as a couple of years could account for the instructor relationship).
We know Gary was a Lieutenant Commander at the age of 23 already, as per his PSI records. We also have reason to think Jim was ahead of him in the game, in a position to request Gary for "his" first command. So Jim probably
is older, although he could still be a star pupil instructor to his elders, or a super student who made full Commander at 22 and therefore could make requests about his older pal Gary.
The issue is basically only clouded by whether Kirk and Mitchell first met at that class, because we know they met 15 years prior to the ep. Perhaps those two are utterly separate events, with Mitchell joining Starfleet specifically because his (potentially much, much older) friend Kirk had already done so. Kirk comes from a Starfleet family, and was friends with Starfleet families like the Mallories. Perhaps he babysat Gary, ten years his junior?
We don't know whether the Republic assignment preceded or followed the Farragut
If both are monolith things, then we do know, as Kirk was an Ensign on the former ship and a Lieutenant on the latter - we can't swap that order. But back-and-forth between ships is an option.
We do know that technically some academy trainees can and do get commissioned as officers even before graduating (Lt. Saavik, anyone?)
What reason do we have for thinking that Saavik had not already graduated?
I mean, it's clear that she had - that's why she's a Lieutenant. But it's also clear that not all officers take the command courses at the Academy (we have characters stating they did not), and not all officers undergo the no-win test, either. It may well be an optional extra, and sometimes cadets include it in their graduate studies, sometimes only in postgraduate ones.
But yes, maximally ambiguous, and frustrating.
Timo Saloniemi