This is actually very interesting. Because you can just turn this around make sure that the person at home leaves their house at that time because someone is coming :) Out of curiosity are you also working on an appointment specific service?
We're still early in the process (much earlier than Patrick is w/ AR), but we've also explored the idea of integrating Twilio. It's nice to see how it's being used.
Edit: it's not a general purpose appointment manager and reminders are not central to my product. More of a basecamp-like app for cleaning services, of which appointments are a part. What are you working on?