Kirk also tries the elevator after being rescued and there is a "D" or "O" on the doors then. ... "they're inoperative below C-Deck".
Never mind, apparently the letters are deck labels, and the Klingons in ST III simply took a wrong turn (before they realized they came to a dead end, turned back and then saw the elevator to the Bridge they had just passed).
But the FP corridor extension on B-Deck still begs for explanation. If only the FP extension suggested a ramp down to the lower deck.
Maybe that scene takes place on B-Deck of the engineering hull (i.e. inside the connecting dorsal pylon)? Better belay that, the corridor there would have to be much shorter, too.
Or we approach the shot from an artistic point of view. Kirk sees the young female lieutenant and suddenly his options seem bigger and longer, he feels young again (metaphorically reflecting in the FP extended corridor). A few decks later McCoy is waiting outside and the illusion vanishes instantly.