[HungryBear]

Ok take that last drawing and instead of employing Grip Rotation you set the face square to the Arc of Approach at Fix. IMO you'd get a straight shot logically wouldn't you? There being no divergence between face and path . A straight shot that is pushed to the right of the Plane Line. You could Rotate the Plane Line to point this push shot at the hole however.

The face angle would be more lofted though wouldnt it? So Im thinking slightly higher, push shot ? Does this make sense geometrically?

Your Plane LIne is open , pointed to the left , but there's no divergence between face and path, face is lofted a tad, straight shot resulting for a ball placed back of low point.

Still talking about the geometric model here.

If you angle hinge and move the ball back on the arc I see a lowe push.
hb