We could make the radius bigger than 1 billion light years, which in turn would make it impossible for you to detect the curvature of the moving sagnac observer within the 1km window. In this limiting case there is very little difference between the inertial and sagnac observers. Why should one measure light’s speed as c, and the other as c+v or c-v?

Just saying “therefore the 2nd postulate doesn’t apply” is an excuse for letting relativity of the hook. Is relativity immune from a limiting case?