So I watched through the Original Series lately, and am now part-way through the movies before moving on to TNG. Looking back, I think I got two out of three right in my initial assessment. Kirk and Spock I am now quite firmly convinced are SLE and LII, respectively. Spock, especially, exemplifies N-LII.
McCoy was more difficult. Obviously he's ethical; that's the root of his whole character. I eventually settled on EIE (possibly N-EIE). The key was understanding the difference between -Fe and +Fe. ESE (-Fe) tries to avoid negative feelings and create a generally pleasant atmosphere. EIE (+Fe) seeks out the best positive emotions, and doesn't mind creating negative emotions if it will result in a payoff of higher positive emotions. I think McCoy's cantankerousness is indicative of the latter, making him either Beta or Gamma. Considering the inter-type relations -- McCoy and Kirk are closer than Spock is to either, making it likely they're in the same Quadra -- I think EIE makes the most sense.
Anyway, let's see:
Kirk: D-SLE
Spock: N-LII
McCoy: N-EIE
Uhura: ESI maybe?
Chekov: Feeling. IEE or SEI?
Scotty: ST of some kind. LSI?
Sulu: Not sure. IEI or something?
Khan: D-EIE, for sure. He's got the classic ******/Mohammed charismatic leader thing.