[Yoda]

Doesn't the hinge pin on the grandfather clock move, since the Left Shoulder is clearly moving during the golf stroke?

How does this fact change anything, if at all?

The Left Shoulder -- the center of the Clubhead Arc -- does indeed move. But, it does so in its own centered arc, the circumference of the Shoulder Turn around the Spine as its Axis. This satisfies the requirements for a Centered Arc and enables the Line of Compression, i.e., the pressure of the Ball against the Clubface, to be sustained (2-H).

This is why the Stationary Head is so important. It provides a major assurance that the Left Shoulder will return precisely to its Impact Fix location in preparation for Impact.