I honestly don't see any difference at all.
No matter how hard I squint.
I'm not sure I would presume the side of the ship so easily, since the shuttles have a tendency to spin on their little turntables before launching.
Exactly. And in fact, if the shuttle rests on the turntable, then a person peering through one of the angled doors marked "ELEVATORS" would see it side on only if the shuttle were rotated at something like 45 degree angle.
In which case the background would not be the clamshell doors, nor the side walls of the bay. The background would be that relatively broad, featureless grey "collar" that goes between the bay doors and the side walls!
How was this done in the "Journey to Babel" and "Immunity Syndrome" remasterings, BTW? Was anything inserted on the live-action background at all? I gather not, since it's not on the VFX reels. Which sort of means that the 45 degree angle thing is the easiest way out.
...And I mean that literally. If one wants to create a redshirt line of honor from the shuttle to the angled elevator door, the most stylish way to do that would be to rotate the shuttle 45 degrees, and have the straight line at 45 degrees to the ship's walls but 90 degrees to the shuttlecraft door and the elevator door.