Another smaller but equally important issue about any re-use of Khan is his attitude to Kirk. In Space Seed, he had no real grudge against Kirk. Kirk and his ship were merely a means to an end, a way of him regaining power. At the end of the episode, there was arguably a degree of grudging respect.
By the time of TWOK, he had spent years on a desert planet and watched friends and his beloved wife die. For which he blamed Kirk. Hence a vengeful Khan on a personal mission in that movie.
If Khan were to appear in any of the next couple of movies, with their TOS time-frame, he won't have the same motivation against Kirk that he had in TWOK and which made that movie so memorable. They'd have to come up with some new reason for him to hate Kirk with that degree of passion and to allow the new actor to bellow his lines with the same amount of venom.