I'm curious about your costs. "The worse case scenario for cost to service that customer is about $20 a month paid to Twilio." Which you say is for 100 appointments per month.
Assuming one text and one call per appointment that's $.04/appointment, or $4/month.
So what am I missing? Does your service let you fan out to 5 users per appointment? Or is that you can send multiple reminders to the same person for a single appointment (24 hour notice, 4 hour notice, 15 minute notice)?