Indeed, a route like this would seem to allow for the drop of three or four decks at reaching the shuttlebay area (red), then a short climb to the desired level (blue) and a flight out (yellow).

We'd just have to assume that the main shaft that serves the secondary hull runs along the top of that hull, in order to allow effortless passage despite the many pieces of bulky machinery and the many large cavities there. A shaft running along the bottom would also serve that purpose, but in this case Starfleet simply chose otherwise.
It wouldn't be difficult to believe that there is no shaft running all the way to the shuttlecraft shelves, either. Kirk's first ship didn't have such a lift, nor did the E-D appear to have one. Our heroes always walked at least one set length to reach that destination - except in ST5:TFF.
We've also seen that people move while "in the transporter beam". In fact, we see that people always move a little while in the beam - that's in the very nature of the visual trick, because the actors in location B cannot assume the exact same pose they held in location A. So we can just as well accept that the transporter is a device that allows the users to alter their bodily stance, their grip of equipment, and so forth, during transit.
Timo Saloniemi

We'd just have to assume that the main shaft that serves the secondary hull runs along the top of that hull, in order to allow effortless passage despite the many pieces of bulky machinery and the many large cavities there. A shaft running along the bottom would also serve that purpose, but in this case Starfleet simply chose otherwise.
It wouldn't be difficult to believe that there is no shaft running all the way to the shuttlecraft shelves, either. Kirk's first ship didn't have such a lift, nor did the E-D appear to have one. Our heroes always walked at least one set length to reach that destination - except in ST5:TFF.
We've seen people beamed up while falling and sometimes they're re-oriented and sometimes not.
We've also seen that people move while "in the transporter beam". In fact, we see that people always move a little while in the beam - that's in the very nature of the visual trick, because the actors in location B cannot assume the exact same pose they held in location A. So we can just as well accept that the transporter is a device that allows the users to alter their bodily stance, their grip of equipment, and so forth, during transit.
Timo Saloniemi