You say that "*turns out that a big part of the job involves regularly meeting with clients and customers*" and then "*So I was asked the initial ‘tell me about yourself’ question but blocked so hard that I had to write on a piece of paper and tell the interviewer that I had a stutter/speech blocks.*" If the company isn't comfortable about your overall communication abilities to put you in this role, what do you expect them to do? You might be super-annoyed about wastage about your time - I get it - it was silly and disrespectful of them to not state their concerns clearly over the phone interview itself. It's possible that your stutter hadn't caused you to block so hard on phone, like it did in person. Clear and fluent communication is a non-negotiable requirement in several jobs, and this happened to be one of those jobs. Tough luck and sorry for the early rejection.