However, this probably would not fit an 8' wide hallway and Kirk's quarters in it.
Unless you put them in sideways. Would also explain why we never see those windows on the walls - they are actually skylights!
Semi-seriously, Starfleet seems enamored with flat structures, most prominently those funny saucers that even on big starships can only accommodate a deck or three. Arranging the interiors in a sort of "urban sprawl" seems to be preferred. And the neck would be a practical flat structure if treated sideways - probably quite a bit more practical than if sliced into decks in the upright position.
"Deck 12" could then refer to the entire neck, from saucer bottom to engineering hull top, and feature numerous curving and branching corridors.
Love this idea conceptually, but it does seem to go against the grain of known Starfleet design. I think there's no reason to assume that any or all of the rectangles on the neck are windows -- perhaps they are sensors of some kind?