Dear Tigersimmo,
With all due respect, I believe that I am the only resource in golf for this sort of information about the body and the shoulder stroke. It's not surprising you haven't found anything looking elsewhere, because I've spent 13 years so far looking myself.
The sort of muscle tension involved in what you describe as a "flat back" is probably about the same as a buck private in the Army standing at attention feels. Good posture has the head riding high above a balanced torso with the chest a little "proud" with shoulders back in line with the ears and the back itself sort of "ram-rod" straight, if you know what I mean. When you preserve this upper-torso posture and its associated muscle tensions and then bend forward at the hips and some at the neck in a putting address posture, I imagine this is about the same as you describe in your question.
Quite a few golfers setup with the arch across the top of their shoulders behind the neck a little tensed, and this tension helps them make a solid and consistent shoulder rock beneath the pivot of the neck. David Leadbetter teaches golfers to turn their elbows inward in the putting setup to help stabilize the "triangle" of shoulder frame, arms, and putter. Your "flat back" posture and tension strikes me as much in the same vein -- a stabilizing tension that helps make your stroke more consistent and repeating.
The more important part of your question in my view is about the plane of motion of the shoulders. You write: "My biggest problem in changing is learning how to tilt the shoulders along the parallel target line." This problem is really unrelated to the "flat back" aspect.
The tilt of the plane of motion of the shoulders does not come from tilting the shoulders a certain way at address, but from the manner of moving the shoulders in tandem. That said, it makes moving the shoulders in a certain way easier and more consistent if your setup contains other body positions as guides or targets for where or how to move the shoulders. There are several guides or targets.
The simplest guide for moving the shoulders is the base of the neck. If you envision the neck as a column supporting the head, the base of the column where the neck meets the shoulder frame is a circular plane. If the head is "flat" or the face horizontal above the ball, the axis of head rotation runs from the center of the base of the neck out the top center of the head, and this axis parallels the surface. That posture orients the circular plane at the base of the neck vertical to the ground. You can then move the shoulders in agreement with the base of the neck, so that the shoulder frame rocks in a vertical plane. This will send the lead shoulder straight down at the ground in the backstroke and then straight up towards where the ear used to be when you were standing at attention.
If the head / face is not flat but is angled up a little so the forehead is higher above the ground than the chin, then the axis of rotation from the center of the base of the neck out the top of the head is also angled up off horizontal to the same extent. This tilts the circular plane of the base of the neck off vertical bottom-edge out towards the ball to some degree. There is an infinite range of possible tilt angles, once we are no longer talking about a vertical base of the neck, but there is one angle of particular interest. That angle aims the circular plane of the base of the neck right at the ball, and aligns the plane of the base of the neck so the plane intersects the ground in a line perfectly matching the putt line square thru the ball. With this orientation of the base of the neck, your shoulder motion is simply a matter of moving in agreement with the base of the neck. This sends the lead shoulder not straight down at the ground but out a little at the putt line itself in the backstroke and then directly away from the putt line in the thru-stroke.
Either way, it's just a matter of rolling your shoulder frame in agreement with the base of your neck.
You don't really have to use the base of the neck that way, and you can setup with the plane of the base of the neck one way and move the shoulders in a plane of motion that is different. I personally sometimes setup with gaze straight, eyes slightly inside the ball, and base of neck angled bottom-edge out a little off vertical, but still move my shoulders in a vertical plane. The flexibility of the body and the degree of freedom of movement of the shoulder frame as a separate component or structure of the body allow this combination without significant problem. In this sort of movement, my target is the balls of the foot located directly beneath the lead shoulder to balance the leaning torso, and I don't necessarily think much about the base of the neck. At other times, the base of my neck is a major guide to my shoulder movement.
But for golfers generally, for the sake of consistency, I recommnend moving the shoulders in agreement with the orientation of the base of the neck.
I would point out two other interesting aspects about this. First, Harold Swash teaches his students that the cervical spine needs to be horizontal to the surface in order for the shoulder movement to be best and generate a pure straight-back and straight-thru action. The cervical spine is that part of the spine that corresponds with the neck, and is what I call the axis of rotation from the center of the base of the neck out the top of the head. I agree that this neck posture supports a repeating straight-back straight-thru shoulder rock, but I don't really believe it is always necessary.
Second, in my system, the gaze direction the eyes aim out of the face (i.e., straight out, or perpendicular to the face), plus a rotation of the head about the axis of rotation, generate a look from ball to target while standing beside the ball at address in which the line of sight of a fixed gaze is carried straight along the ground in a reliable, accurate targeting process. This head-eye posture may be a "flat head" or a forehead-up tilt. In the former case, the line of sight turns in the manner of a Ferris Wheel. In the latter, it turns in the manner of a Tilt-a-Whirl. Both deliver the sight straight along the ground. But the interesting thing is that this beside-the-ball targeting "look" uses the base of the neck like a "clutch plate" between the moving head and the still shoulder frame. This targeting "look" makes you very sensible about the orientation of the base of the neck as a "plate" or circular plane. Hence, once the "look" is completed and the motion shifts to the stroke, the head now remains still while the shoulders move in a plane. Again, the base of the neck acts like THE SAME "clutch plate" -- this time between the still head and the moving shoulder frame. That makes the targeting look "teach" the shoulders how and where to move, in agreement with the base of the neck. The targeting look dovetails perfectly with the forthcoming stroke and gives you almost a cheater's preview of how to move the shoulders. Look (feeling the base of the neck), then fire (repeating the feeling from the opposite side). Simple.
Finally, I would emphasize a totally relaxed setup posture. If making you back "flat" adds tension, I would prefer you learn to putt without the tension. If leaning over at the top of the spine to get the head flat adds too much tension, I would say to relax and not bend over that much but still keep the eyes gazing straight out. You can end up with a VERY relaxed setup posture and still use the base of the neck to guide the shoulder movement. This gives you three basic choices:
Setup with a flat head and move the shoulders vertically in agreement with the base of the neck (like Swash teaches) and use the balls of the feet as movement targets complementing the movement in agreement with the base of the neck;
Setup with a head slightly up, eyes inside the ball, but gaze straight out, with the circular plane of the base of the neck angled out to meet the putt line, and move the shoulders on this tilted plane of motion to and from the putt line as they rotate about the axis of the neck; or
Setup as in the second manner but move the shoulders vertically to and from the balls of the feet, even though this is not the same as the base of the neck.
The added tension of the "flat back" may be something you rely on while working in the direction of a more relaxed and confident shoulder action. That's fine. The tension will do double duty to prevent you from using the wrong muscles to make the motion. The wrong muscles are those right at the shoulder joints, at the pecs, and across the top of the back. The correct muscles are the ones that move the whole upper torso, and they are the abdomenal and lower back muscles that connect the upper torso to the lower body in a pattern that spirals down from upper to lower skeletal features. The "flat back" tension may be modest, but the body reads the tension so that it remains steadily the same as the putt stroke progresses. In that sense, it is like setting one grip pressure and then keeping it steadily the same tonic pressure during the stroke. The back tone is similar in function. because of this, the same way golfers "milk" the handle to set their grip pressure at a known / felt level can serve to "set" the back tone in your "flat back." The end result is a stability and a closing off of using the wrong muscles and sort of forcing you to use the proper muscles. Ultimately, though, you can eventually get to a truly relaxed setup posture of pure comfort, so long as you know where and how to move the shoulders when it's time to pull the trigger.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
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