I'm not convinced that you can go from Cat 1ILS down to LLZ only. Surely the reason for using the next level is in case there has been a failure in the better facility.
In the case of a Cat 1 ILS you could have lost the LLZ, hence imho you must go to a non-ILS based approach aid, so to a VOR/DME, NDB/DME, PAR etc.