Dear Mark,
It sounds to me like you are cross-dominant -- right-handed but left-eye dominant, like Jack Nicklaus. Golfer like this perform better with a slightly open stance. The slightly open stance allows them to have a sense of the left side of the body moving towards the target or reacting to the target, which is not available when the shoulders and feet square to the line.
I've written about this before in the Forum and the basic choice comes down to whether you remain open after aiming the putter face or whether you thereafter square back up for the stroke. It would be nice if you could aim open and then square up and make the stroke, but that is something for you to experiment with. By "open", I mean just a little pulling back of the left foot from the square toe line.
Part of this may be the way your hips relate to your shoulders. Not everyone can address a putt with hips square to the line. Over your life, you may have developed a manner of walking and standing such that when you address a putt, your hips want to be open, or else you feel cramped. The hip alignment can affect the shoulder alignment without you being particularly aware of it, and this can cause pulls. If your hips are open but your shoulders square, then that fits with Jack Nicklaus and other cross-dominant golfers.
Fundamentally, it is the top of the body that putts, so this bears more attention.
Check your eye dominance and let me hear back.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
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