As I said before I am a current simulator instructor on the NG and Max. I am not authorized to say who I work for. For clarification the customer has the HGS on NG and Max on the LHS and it is sop to use it. Further complication with cat 3. NG authorized for cat3a with HGS. Max authorised for cat3b but no HGS allowed. This may be a regulator driven issue and I am not sure why. The Fail Operational autopilot has Rollout mode and the root cause of the above runway excursions may have something to do with that or not as I am just speculating.