First question, yes, but I suspect you've confused things a bit. 7.6m/7.6m
is the spec accuracy for WAAS. Measured accuracy is <3m horizontal, high-end systems about twice as good. Vertical accuracy is not good enough. Cat III will require <1m accuracy. The proposed, well, in development system for Cat III approaches is currently called LAAS (Local Area Augmentation System) They're both forms of differential GPS (dGPS).
LAAS works a lot like the old dGPS. dGPS was to transmit correction data on the piggy-backed signals of high-powered FM stations. Two problems: it degraded in accuracy the further you were from the station limiting its certified accuracy to 10m and, high-powered FM stations tended to only be available in large metro areas. This limited its usefulness for long range navigation even in the con-US. It also had the problem that you had to have a separate receiver for the differential data and a plug in your GPSr to accept that data, meaning everybody (land,sea and air) had to upgrade their equipment including the manufacturers. WAAS got around that by piggybacking on a GPS signal and using geosynchronous satellites to deliver the correction data.
As I said, LAAS uses the same concept, but with a few extra twists. Each LAAS-equipped airport will have its own augmentation reciever stations and serve as its own master station and corrections transmitter all-in-one. It won't be dependent upon GEO satellites. This should mitigate the high latitude deficiencies of WAAS. It accepts the range limitation, even embraces it. By limiting the certified range the certified accuracy goes up. You'll still use WAAS for route navigation. One piece of technology can serve the whole airport and because you wouldn't be following a beam, straight in approaches aren't neccessary. Every runway could be Cat III as long as they met the lighting, etc. requirements.
