Personally, I like to divide the turbos and everything else into thirds in the saucer. It just seems more tos in style. On the other hand, it doesn't jive with those compartment things.
...along with all those door-opener people. This explains the large crew size.
People often complain that the ship wastes too much space via the large corridors, but I'd wager that most of the ship's machinery and structural framework is actually crammed into the walls...
200 crew, and 230 door-openers! That explains the difference between Pike's and Kirk's crew estimates! By jove, I think you've got it!
(Apparently, Pike considered these people "steerage."