It shouldn't be too hard to throw together a side view, but it is all going to depend on how close to the other hull you place the cabins. Hold on, here we go, three possible options:
Obviously I am guessing a bit on the angle of the upper saucer, but you get the gist; depending on the shot (and how much we see of the upper part of the corridor) it may indeed be possible to nestle the cabins into the sloping hull.
However, the ceiling in the cabin would certainly be visible, which would not match any onscreen representation that I am aware of. Perhaps for (unseen) crew quarters though?
As for the ladders - maybe they lead up into the Enviromental Engineering machinery, rather than across decks?
Finally, since it had to be brought up somewhere and since you've already mentioned Sulu's climb in TNT, what are we to make of Uhura's line:
Sir, level two, corridor three reports a disturbance. Mister Sulu chasing crewmen with a sword.
Does "Level 2" mean "Deck 2"? If so, where? The section of corridor we see does not fit comfortably into the deck section below the bridge. If it is on Bob's Engineering Deck 2 this places the action in the Pylon, where there is even less space!
Where oh where did Mr Sulu do his antics?