Beamed propulsion of a light sail based on radiation pressure benefits from a passively self-stabilizing "beam riding" diffractive film. We describe the optomechanics of a rigid non-spinning light sail that mitigates catastrophic sail walk-off and tumbling by use of a flat axicon diffraction grating. A linear stability analysis and numerical integration of the coupled translational and rotational equations of motion are examined. Stability is traded against longitudinal acceleration. The examined system achieves 90% of the theoretical longitudinal force limit and stability against a relative sail translation up to 30% of the sail radius when the payload is attached to a long boom. Administration (NASA, Innovative Advanced Concepts Office), Award Number 80NSSC18K0867. We are grateful to Ying-Ju Lucy Chu and Amber Dubill, Rochester Institute of Technology, for discussions related to radiation pressure and rigid body dynamics, and to Les Johnson and Andy Heaton, NASA Marshall Space Flight Center, for discussions on light sailing.