Thanks, MistressEll, for the information! I really appreciate that you took the time to look into this. I must admit -- we're past desperation and are starting to refer to our house as the Amityville Horror. We had hoped to have our house listed by now!
We also finally got some information back from GE. They claim replacement for our switches is the RS 2-xxx series -- for us it's RS 2-32 (or 2-37 or 2-39 depending on color), but then you need a new faceplate model RP2-xxx. They look similar to the Remcon switches that Doug referred me to.
We also gave in and are hiring an electrician for all this -- to ensure the relays and switches are both actually working. We assumed that all the switches were having problems because one was definitely broken, but it may be that some are relay problems instead.