This could possibly help
One Plane and Two Plane Golf Swings
Last I checked I had a one-plane swing. May sound funny, but I don't really think about it and didn't know that I had converted until a few years ago when an instructor told me. Your logic sounds about right, and when I tend to hit my driver poorly it is usually that logic that I have found has me moving to far away from the ball. Check to make sure you are not extending your arms out as part of the process. I do play the ball a bit further back from my left heel, otherwise my control get erratic. Usually high hooks or sometimes big bananas starting to the left
In other words, don't make your arms part of or an extension to that circle. That would be more of a "Natural Swing" from what little I understand of the Natural Swing.