Canon has no rooster in this fight. James R. Kirk and James T. Kirk are both canon, they both appeared on screen. Continuity and canon are different animals, and continuity is very fluid where Star Trek is concerned. You forgot the third option: that everything is you mention is "right". I have books sitting on my shelf, officially licensed, that state TOS takes place in the 2190's. You just have to get used to the idea that the writers never took this stuff as seriously as we do. From my perspective, TOS was first in, so it is the last out.