The cornerstone was moved into position with the forklift, and then the forxlift changed position to give it a diagonal approach to the framework. The corners of the frame, the corners of the stone, and the forward path of the forklift had to be perfectly aligned. There is an unavoidable jerkiness inherent in the movements of a forklift, even with a good operator. A stone with this much mass could crack itself against the rigid frame if it were not perfectly aligned.
The project made us all marvel at the genius of the ancient peoples in shaping and moving such massive objects without modern machinery. I think the answers in that line of puesuit are in the area of those people "feeling" the masses in the stone and knowing where the least force will accomplish the most work. That is, having your head deep in a rock.