When I started with PuttLab, the most common stroke pattern we saw was a small to moderate arc tilted left. Visually, to many tour players this looks like straight back and straight through. Although it is really straight back and straight to impact, and then the putter swings inside to follow the plane or the arc defined by the plane.
The common release was the hold or not to let the toe catch the heel of the putter through impact. Because they couldn't measure the exact position of the face relative to the path, what they called square was really a little open to the path. It was hard to explain to them, as feel is real to the tour player and many didn't like the idea or thought of a cut stroke. Even though it is not really a cut stroke because of the elliptical nature of the path. The visual appearance of an arc happens when the putter is no where near the proximity of the golf ball. So if you judge path by the follow through you think 1 or 2 degrees is huge. Look at this diagram. While the face is square to the target line it is open to the path of the putter at impact (blue circle). But try telling that to a successful tour player.
For me the proof came when we started to look at a number of putters built by one famous builder. Many of the grips coming out of his studio were placed so if the flat spot was on top, the face was slightly open 1 or 2 degrees. So if you can picture the putter coming off the bottom of your arc and starting to swing left as it comes into the ball you can picture how an open setting of the grip would help hold the face square to the target. If the putter is moving 2 degrees left of the target at impact, then the putter face should be 2 degrees open to the path to be square to the target. Picture the grip of the putter parallel to the red line. If it was installed "open" the face would be in this position.
When I started to point this out in my travels, there was a bit of a commotion. Not from the players, they were aware and liked the idea of making a left miss more difficult. The commotion came from the perfectionist instructors and players who thought the perfect stroke would make you better.
My recommendation for right now is to develop a complete understanding of your stroke without the pressure of results. Use your outline and try to get a picture of your stroke and release pattern. You will find when the new putter comes there will be some adjustment, that is why I would rather you set results aside and just judge the movement. Think, "What pattern of putting stroke is best suited to my new putter?" The new putter will help you take care of the rest.