I have to say, due to Takei not being in every
episode of seasons one and three anyway, his slightly extended absence from season two isn't perhaps as noticable as it would be if he'd been contracted for more episodes in the first place.
For the first season, Shatner, Nimoy, Kelley, Whitney, and Takei were all signed as "series regulars."
It always made sense to me that Kelley, Whitney and Takei were all contracted as regulars (or 'semi-regulars'). Whitney is there front and centre alongside Shatner and Nimoy in the early publicity material. Of course, that could just be because she's a pretty face. Not to say Nimoy and Shatner aren't
... oh, you know what I mean.
Just out of interest, what were the terms of Doohan's contract? I notice you don't mention him, but as a carry-over from the pilot episode like Takei surely he would have had a similar contract?