You aren't alone. However, I'm deaf myself. I had been in speech ever since I was into a school so young - around 2 at the most. I had to go to speech twice a day and it drove me crazy. At most point, you are correct, we NYers tend to speak fast because no one wants time to be wasted! (lol, if you have seen the way they drive, you'll know how they will speak most of the times, not always). Anywhoo, I tend to stutters only if a word that is rarely used or unheard of for me. I think what it is that we rush ourselves too much these days, we need to slow down and speak. I would inform others to let me think a minute and they accept it. Once I have my thoughts gathered or clearer thoughts, I'm able to communicate more fluently.
From my experiences, people are usually in a hurry and don't have a lot of patience. The best thing we could do is clear our mind and refresh ourselves. I would not worry over it too much since we are at a physical disability that others don't have at our own level and experiences. They hadn't or haven't been through what we went through. You know what you are capable of it and stick with it.
If anything, I don't ever want to step back to speech therapy. I give myself a few rules when socializing - which also helps for public speaking.
1) Hold chin up - which allows speaking to be much clear and sound travel well enough.
2) Take your time - if you rush, you will continue the same mistake and make it worse
3) Breathe, physically and mentally - you will be able to calm yourself and relax your ability to speak with others
4) Remember you are human - you are human and humans make mistake, there is absolutely nothing wrong with you.
5) Think before you act (or in this case, speak) - thinking helps to handle situation better and make it easier for everyone, including yourself.
I'm not sure if my rules - or structures- would help, but thought to mention otherwise.