If you have osteoarthritis of the C1-2 joint (not common), a C1-2 fusion can help relieve headaches but the price to be paid is 50% loss of head rotation. That is a high price to be paid if you are wrong. It is highly unlikely that you have ligament laxity without a disease process like Ehlers Danlos or Morquio’s syndrome or have Down’s syndrome.
Overhang of C1 on C2 is quite common with rotational views and does not indicate instability. See this article: https://neckandback.com/conditions/stabilizing-ligaments-upper-cervical-spine-occiput-c2/
Dr. Corenman