The possibly radical opinion I've formed on this (in a thread last year sometime) is that the reset performed by TWoK in reaction to the unsuccessful aspects of TMP was so complete that there was no refit. That is, the TWoK Enterprise is simply the old TV-series Enterprise as it would have looked in the 1960s had there been the budget for it. This, of course, fits with the vessel being sufficiently used-up to be judged a candidate for the scrap heap in TSFS.
In this framework, all efforts to position TMP chronologically before TWoK are futile. Kirk isn't back at a desk job in TWoK after captaining (admiraling?) the Enterprise in TMP; why would he be? He wouldn't - in fact it's the same desk job at more or less the same time point. (The only relation to any past event is given as "15 years after 'Space Seed'").
I've gotta say, I've (slowly) come to the same opinion. Obviously we as fans have to find a way to try and ret-con events between the two so that they fit together...
IMO, I don't think there's anything to retcon at all. TWOK takes place more than a decade in-universe after TMP. Now, we can conjecture
what happened between the two films, but enough time passes that the idea that Kirk returned to the admiralty and Spock took over the Enterprise
at some point prior to TWOK isn't that implausible a concept, and even seems a likely one.
...but stylistically it appears that Nick Meyer more or less worked from the blue-print that he was overwriting TMP, not trying to sequelize it. .
There does seem to be a case to be made for that, especially given that the TWOK originally wasn't going to be numbered.
The fact that "II" is in the title is a clear indicator that it's at least acknowledging that it's the second movie. Whether this adds anything or not, I used to have a Leonard Maltin film guide where he reviewed, what seemed like, every movie in existence up to that point -- in this case, the one I had was from 1998. On his Star Trek II
review, he mentions the film was released as "Star Trek: The Wrath of Khan
That's not true, is it? Was the "II" ever omitted at any point? I've seen the original trailers, posters, and TV spots and not once did I ever not see the "II" in there.
I wasn't born yet when the film was released, so.
The original print of the film wasn't numbered, but subsequent prints were.