The MD-80 was Cat IIIa; Fail Operational rudder is the key to IIIb. I remember engineering at McDouglas wanting Fail Op Squared for the rudder, whatever that is, for IIIb.
Didn't the 737ng get the Collins Triplex Autoland system like the other Boeings when they went to IIIb? Up to that point, they had dual Honeywell Fright Guidance system, same as MD-80.
GB