The Captain's failure to initiate a go-around from a Category III approach when satisfactory tracking performance was not maintained below the required altitude resulting in excessive bank angle maneuvers at low altitude. Factors contributing to the incident were: The Captain's decision to execute a Category III autoland approach on a runway without rollout guidance contrary to company Flight Manual guidance, the Captain's decision to deviate from the Category III approach and continue it manually contrary to the company Operating Manual, and the First Officer's failure to call for a go-around when the approach became unstable.