Doesn't invalidate the idea of Kirk visiting him. He just didn't tell Chekov that Khan was now suffering, and probably soon dying, on a true hellhole of a planet.
Anyways, the 3100-range stardate of "Space Seed" might well indicate the third year of the five-year mission, thus something like 2268. Add 500 stardates for six months, assume the dates begin when the Desilu season does, and 3700 might well be past the 2269 mark. Fifteen years would get one just past the important ST2 milestone of 2283 on McCoy's bottle, then, without the need to play with rounding up or down...
I wonder... What technologies did Khan have access to? Apparently nothing he could build an interstellar communications device or a spacecraft out of. But did he have things like groundcars or aircraft, or was he denied even basic water purifiers?
What is this thing?
Or this one?