Gavin,s old stroke was based on concepts that many amateur golfers hold as true.Trying to keep the putterface square to the target line and trying to rock the shoulders back and thru are concepts that just dont make sence biomechanically. Good putters have common denominators, there strokes are mechanically simple,they have proper path and loft. Rolling the ball correctly requires these two things.
The things that create path and loft are Posture and how the arms or more specifically the angle of the arms and shaft relate to the posture at setup. Just Like the golf swing if Gavin is not setup with the correct angles it is impossible for him to move in the right direction.
We have done alot of work on his posture, bending from the hips and maintaing a straight spine, this allows him to turn on the angle of his spine, without good posture it is impossible for the body to turn in the right direction.Gavin used to have a hunched back and buried head at setup. From behind his foreams and shaft now form one line. This basicly allows him to create a one lever system in three dimensional space. His arms and putter are contolled by the turning of this torso around his spine angle.Notice his eyes are slightly inside the ball. Most great putters do not have their eyes over the ball as it encourages the shoulders to turn to far under and the spine angle to change.

You will notice from the side view his arms are bent at the elbows and his hands are both facing each other. It is important that the hands go on the putter in a neutral position, if they are not they will try and get back to neurtal during the stroke effecting the angle of the of putterface. In Gavins old stroke his left wrist used to bow the other way ( no angle in it) which used to shut the putterface on the way back. People who forward press their hands or try and keep the putter square to the target line on the way back will deloft the putterface. Ideally the shaft should point infront if the belly botton at setup.

From the front view you will notice the shape of his arms doesnt change throughout his stroke . This is because his arms and shaft are setup in such a way that they remain in the same relationship to the body at all times. This keeps the putterface square to the body as it turns on its angle.
Most people are always working on what the putterhead does,I believe it is just on the end and cannot be contolled without changing the things that effect it. Trying to move the putterhead straight to straight will cause it to get high of the ground on both sides of the sroke, create changing loft during the stroke and ignores factors on which the stroke is based such as putter lie angle and the natural geometry of the body. Gavins model stroke is not complicated it is something that everyone can achieve if they understand Setup and how the putter relates to the body. The correct seqence can only be achieved if the start is correct. The stroke is just too small there is not enough time to fix bad motion up like we do in our full swings.