As the saying goes, "Where there's profit, there's a way". If you feel that being in breach of Twitter's terms of service will get you shut down, you need to devote everything you've got to finding a solution where they don't can you, but you keep your revenue model. Maybe it's hard to hear, but I'd suggest trying harder to get a meeting with them, or hiring someone as a go-between to set up a meeting. Also, a technique that a friend taught me is to connect with the person below your actual target in the company, and build a relationship with them. Then they will help you set up a meeting with the person you actually need to talk to. (btw, they call this the Cheerleader tactic.) Good luck!