I'd agree that the movie was always supposed to take place about a decade after TOS - or more exactly, it was written following the idea that Star Trek takes place exactly 300 years after the respective episodes and movies, an idea adopted in the fandom soon after TOS folded. This is why e.g. the Voyager probe was launched "more than 300 years ago" - it's 2279 "now", while the first Voyagers launched in 1977 for real.
Modern references force us to adjust that ever-so-slightly, in that we know (from TNG "Cause and Effect") of a different type of uniform being in use in 2278 already, aboard a ship that already has the "modern" engines of the Enterprise
and thus makes it less plausible that Kirk would have so much trouble with them at a later date. But 2277 or so ain't a bad date for ST:TMP.