Interesting, thanks for the reply Pete. It looks like I'm going to have to try some pretty unconventional methods here.
When I mentioned that WeatherRemoveStation has nothing to do with the ATIS, I meant actually removing an ATIS from Flight Simulator. The thought was to try and remove the weather station for KSFO, and see if that also removed the ATIS along with it, so that you would no longer hear any KSFO ATIS on its ATIS frequency. However, after reading, it appears that you can only remove Weather Stations that you have previously created in SimConnect, so it is my understanding that you can't remove any default weather stations that FSX has already generated, since you don't create those in SimConnect. Please correct me if I'm wrong.
Do you know how Radar Contact disables the default ATC? I had VoxATC for FS9, and I remember having to disable the voice slider in order to eliminate the ATC, but as stated, that doesn't work for my situation.