Why can't your techs change how many times a phone rings before going to voicemail? My phone rings three times, then voice mail picks up. No time to answer if I'm in another room.
The ring time is set at 30 seconds at the system level and can't be changed. Perhaps you can try a different ringtone. Sometimes that helps. Personally I prefer one that is has the same volume level throughout the sound or louder at the beginning. Ones that ramp up the volume before repeating doesn't seem to be heard as quickly for me.
Or you can just simply call the person back when you see that you missed a call.