Yeah, I'm unconvinced....Long story short (too late?

), the only hard-and-fast chronological relationships between TOS episodes and original-crew movies are (A)
TWOK happens fifteen years after "Space Seed," and (B)
STV:TFF happens at least 20 years after the end of season one (since the Nimbus III colony could not logically have been established until after the Romulans were back on the scene in "Balance of Terror,"
and the Klingons had been reigned in by the Organian peace treaty in "Errand of Mercy"). It has always struck me as quixotic to disregard one of those relationships for the sake of otherwise completely arbitrary dating conventions and far more ambiguous evidence. FWIW, in my own timeline (headcanon of course, but very detailed) I place these two films in 2283 and 2287 respectively, with a significant time gap between movies 4 and 5.