I suggested it before, but I think you can work around it: Let your customers give you their Twilio API key (with a big disclaimer that any charges by Twilio are not your responsibility...).
That would be the nicest user experience for your users, but it is a bit risky. You probably have a "reasonable number of notifications per user per month" in mind. As you sign up new users, you will sooner or later get some that will exceed that number by a lot--without a malicious intent.