Most of these gel pretty well with what I've always imagined (except for a second 5-year-mission. I've never seen the need for it.)
Between TMP and TWOK is when Kirk left Starfleet, got the cabin in the woods, and met Antonia. When he told her he was going back to Starfleet, it was to be an instructor at the academy. Kirk was never the Admiral in charge of the academy.
Actually, it was never said that Kirk was going to be an instructor at the Academy. He just said that he was going back to Starfleet (or at least wasn't going to settle down with Antonia). The timeframe given places his time with her just a few years before TWOK.
But as this thread is about personal continuities and not about canon
, it doesn't matter. Kirk was Commandant in mine and was the reason he was loitering around the Academy and went on a subsequent cadet cruise.
There's no wrong or right answers in this thread.