Do the actors' physical changes need explaining at all? There is no real justification for the complete change in visual aesthetic between TOS and the movies either, except to say the producers changed and updated how Star Trek looks. An Enterprise refit doesn't cover the complete change in the Klingons, for example. Or that not a single computer console, keyboard layout or screen readout in any way resembles those seen in TOS.
...the very reason the only sensible explanation is a ten year gap; in that time, actor/lead characters' physical appearance and technological changes can be easily explained (for example, think of car design in 1959, then jump to 1969, or rocketry in 1947, then think of the advances in use by 1958). Major changes happened in real 20th century decades of growth, so it should not be an impossible feat at all in the fictional late 23rd century
On top of that, audiences simply cannot forget what is seen in front of their faces, which is why fans in '78 (one year before TMP release) assumed the film was as removed from the series in the same amount of years as real life. The actor and design changes would be plausible in a stretch of ten years.
The Klingon issue is another matter--one so going against a natural explanation of evolution (and at the the time, no one thought of the retconning created decades later in "Trials and Tribble-ations"
) that it stands as the one issue that cannot be easily explained away. That is, if Roddenberry, et al, did not think of simply saying the species was hit with some form of radiation--even genetic experimentation were responsible for the physical changes. That would have been the easy put-away for the Klingon issue.
But in TMP, everyone's active and it ends with them warping off to new adventures (the apocraphyl second 5-year mission - after all, TMP began life as the pilot episode for Star Trek Phase II). Then, in TWOK, the crew are split and those remaining are in the twilight of their careers, training the next generation of Starfleet. They only reunite on the Enterprise for "a little training cruise"
Back in the old Best of Trek books, there were fans who believed TWOK deliberately ignored TMP, and others that felt the movies were incompatible.
That was their choice, but it was not on screen. At the end of TMP, with Kirk's "thataway" line, I feel that was more for the audience (a "we will be back, fans" tease) than any official, hammered in stone notice of Kirk and company all reassigned to the Enterprise for another 5-year mission. It is not said, and V'Ger was the only reason they were together again.
There's no official post-TMP 5 year mission, so i'm assuming the Enterprise returned to spacedock to complete its renovation, or perhaps it was destined to be what it was in TWOK: a training vessel. After all, one film later in TSFS (same period of time), the Enterprise is considered too old, and is destined for mothballs, which means both details (training ship and its age) probably means it was not used as an exploration ship post TMP.