Part of the problem of aligning putt 10" and under is you're sort of too close to the hole. Try standing pretty far back from the ball when you align from there. On a 10' putt, stand another 10' behind the ball. On a 6' putt stand 6-10' and on a 4' putt stand 6-10' back.
Then when back there, use your putter shaft as a visual ruler that connects the ball with your target spot (lip or point beside the hole). Let the "ruler" divide the ball in half and look for spots in front of and directly behind the ball.
Also, from back there, when you look at the back of the ball it has the appearance of a circle. The exact dimple you will want to contact at impact is located in the very center of that circle. So when you walk into the ball to address the putt, you will want to make sure you know where that dimple is so you can square your putter's sweetspot directly behind it, aimed squarely thru the ball's center. I look for some writing on the ball to help me see this one dimple, and if there isn't any nearby, then I look for a discoloration on the grass below the center of the ball.
When I walk into the putt, I try to keep my dominant eye on the line as I walk and sometimes I keep my visual ruler held up so I know I'm not wandering off the line. Then when I get to the ball, I set my putterhead sweetspot centered on that one dimple. Then I have to make sure the face is squarely aimed thru the center of the ball and this aiming is the direction I want the putt to roll. To do that, I realize that two points are necessary to make a line. I have about five or six points, all on the same line - one behind the ball, then the dimple on the center of tyhe back of the ball on the equator, the top of the ball itself, the dimple on the front of the ball opposite the back dimple (like north and south poles on the globe), and a spot just in front of the ball on the grass. All of these spots need to be in one line, and this is the line I want to start the ball rolling on. So I manipulate my putterface (twist left or right) until it looks perpendicular (right angle) to this line thru the center of the ball.
If you want to, before you place the putterface, you can walk into the back of the ball, mark it, and then line up the logo or other line on the ball's equator in the direction of the start line of the putt. Than go back to where you were, check the alignment, walk into the ball again, and (if satisfied) place and square the putterface behind the ball. Personally, I skip this part.
In any event, once the putterface is centered and squared behind the back center of the ball, this arrangement allows one and only one stroke that is straight -- the sweetspot of the putter with a square face must move thru the back dimple, the center of the ball, and out the front dimple of the ball. This is ALWAYS true in every putt. In other words, once you have placed the putterface the way you think it ought to be aimed, you're done -- nothing left to do except make THAT stroke straight thru the ball.
I know this procedure really works (assuming you have read the break and hit the ball with proper speed), but you may nevertheless not trust it to work, or feel uneasy about the situation. Most of that is just a cloudy mind about how it works. To convince yourself, you have to practice straight putts. So find a level stretch of green and putt to a tee peg 8' to 10' off. Use the full aiming routine.
If you still feel uneasy at address, then it is probably because the way you are checking how things look from there is not a good way to do it. The tilt and angle of your head and eyes from address is likely causing you to sense the target is somewhere other than where it really is. This makes you second guess in mid stroke. The cure is to line up properly, and commit to making a straight stroke NO MATTER WHAT- even if you are sure a straight stroke will miss. Go ahead and miss! It is only by training yourself utterly to commit to making a straight stroke that you will ever get a handle on your aiming problems.
If you still feel uneasy from the address position, then you have to fix the way in which you target the putt from beside the hole. This is mostly cured by making sure your gaze is directed straight horizontally out of your face before you bend to look down at the ball, and then when you bend, keep the gaze straight out of the face until your gaze is vertically looking straight down but still straight ahead out of your face. Then when you turn to locate the target, your gaze will have to run in a straight line across the green, the same straight line your putterface aims along. You'll probably have to read my tip "Gaze Dead Straight for Dead Aim."
The long and short of it is: aim well and conclude your aiming process by the way you orient the putterface behind the ball; make THAT straight stroke and nothing else, with good tempo and speed. Any thing you want to do to reassure your aim or double check it from beside the ball has to be a good aiming procedure, or else you will substitute fool's gold for the real thing.
Looking again at your questions, let me address specifically two -- checking body alignment, and stance open or otherwise.
Once the putterface is aimed, your putter is resting flat on the ground on its sole and its lie angle makes the handle stick up a certain way. Your job is to set up your body to this putter as it rests there. So, never grip the putter until after you have oriented the putterface. Even then, get your sense of tyhe startline and set your shoulder joints parallel to this line, and your feet should "toe the line" parallel to the putt's startline also. Once your feet and shoulders are square and parallel left, you can set your eyes over the ball. Actaully, setting the feet, shoulders, and eyes happens all as one addressing the putt required by the putterface setting. Once your head and eyes and shoulders and feet are all set, you can let your hands and arms hang naturally and relaxedly down, and THEN take up your grip on the putter, however low on the handle that may be. Your good setup determines how low on thew putter your hands fit, not the putter handle's height.
So I recommend a square setup, not open or closed.
Checking the squareness of your setup is really about using your eyes so that your head and gaze directions while "looking" (turning) toward the target or down the line do not feed you incorrect impressions about the target location. This is my tip "Gaze Dead Straight for Dead Aim." When you know how to use the eyes as described in that tip, you will be able to use your gaze and your head turn to check whether your square setup to the ball and putterface is, as a system, also aimed along the ground where you need the ball to start out. In other words, the eye procedure allows you to "see" where your setup is aimed. If the aim is true and the setup square, the only thing left to do is make a straight stroke straight thru the center of the ball with a square putterface, using good tempo and speed.
Not too complicated.
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