Yeah, that's the big error. I intended to fix it by arranging the turboshafts a certain way. But I actually think I made a mistake, too. My engine room is backwards from how the captain apparently moves between the turbolift and the shuttlebay. But there's not really any reason why it has to be one way or the other. There seem to be some slight inconsistencies with the set pieces he moves between, so there's definitely some room for interpretation.
My interpretation of the cavernous engine room shows 4 turbolift shafts. I imagine that the captain is descending down the third one from the left. Gives him quite a way to walk, I guess. But there's no reason that he didn't board a second turbolift that runs sideways straight to the staircase he trots up into the hangar. Displaying only one single slice of the ship, it's hard to show stuff like that. But we can imagine it's there.