There is no stabilization of the flat spot without neutralizing the impact of the changes in the body planes during the golf swing motion. These changes are inevitable taking into account the way humans are built. The most dreaded are the movements up and down of the body and arms. The flexion and extension movements in knees and elbows (up and down in golf so to speak) seem to be of critical importance, however, the spine side movements cannot be underestimated. Ideally, the setup position should match exactly the impact position but in theory only. Last but not least, the inventor of the flat spot concept, Mr. Phil Rodgers, wanted us to limit the up and down movements in the knee joints while not letting them to flex too much so that the spot was as long as possible in the impact zone.
Let us see what joints are the most vulnerable (red) for transverse plane movements from the ground up -- knee joints and elbow joints (for golfers practically only rear elbow joint as the lead one is not supposed to be in a flexion). Stabilizing their flexion/extension movements during the motion is of critical importance. As shown on this beautiful image of Ben Hogan from his 5L book, there are also joints of secondary importance in this matter (orange), such as ankle, hip and shoulder joints. What is great, it is easy to take control on these joints while we work on knee and elbow ones.