It really isn't that hard, you are over thinking it, forget the minima page on the plate, for CAT3 operations you fly to whatever your company specific CCI page says.
Fail operational (CAT3 DUAL in Airbus speak) and fail passive (CAT3 SINGLE or CAT2) aren't associated with any specific minima, they are the operational landing capability based on the technical state of the aircraft.
If you have CAT3 DUAL on the FMA you can operate down to whatever CAT3B minima are included on the CCI page, if you have CAT3 SINGLE you can only go down to CAT3A minima and if CAT2 down to the CAT2 minima on the approach plate.
BUT be aware that some failures that downgrade landing capability are not sensed by the aircraft (Windshield heat, standby horizon etc.) so with a failure you must check the required equipment table to check you still have the required landing capability.