but it looked too far east to me to be riding up one of the future elevator shafts of the west tower.
They don't use the elevator shafts for the cranes. Look at any site and you'll notice the hole for the crane is only large enough to fit the crane. And this size is too small for an elevator. Also notice that there's generally no other openings close to the crane. Elevators are located next to each other so you'd expect to find additional openings right next to the crane.
Check this photo of X. Elevators are in the core area. Cranes are further out.
I know how cranes grow at the top, but wow exactly are the bottom of the cranes hoisted up from floor to floor?
The concrete pad on the ground seems good enough to hold up a crane, but once you start to jack it up onto higher floors, what's holding it then? How do you even lift the thing up in the first place?