I know just what you mean. I've been a moderate/severe stutterer all my life, and I come from a long line of stutterers, passed down the maternal line.
Yes, emotional state and fatigue make it worse, but I've found that facing fears about stuttering in social situations has been the largest help in "getting over" it.
High school graduation was rough. I had practiced my salutatory speech until I was fluent, and I practiced in front of small groups of people, but when I faced a crowd of thousands of people in Reunion Arena in Dallas, all the practice went flying away. I stuttered and stammered through the entire speech. When I received a standing ovation, I didn't know if they were congratulating me or just massively relieved it was all over, but I did not know then that the worst speech event of my life had just passed.
Was anxious over high intensity social situations, but I learned I live through them. In college, I dated a very high powered girl who was the chair of the Endowed Lecture Series at Texas A&M. One time I was her escort to a reception following a lecture hosting Henry Kissinger, Zbigniew Brzezinski, and a number of other foreign policy luminaries. I was so anxious about the speech situations, as she quietly pointed out the rich, famous, and powereful to me, that I didn't notice Henry Kissinger near me. I whirled around to help with some detail, and I ran over Kissinger, knocking him to the ground. Hey, I just messed up a social situation, and I didn't even have to speak to do it!!! He was very gracious, but for some reason my girlfriend did not have me escort her to any more receptions. Oops.
I received more speech therapy in graduate school, and that's where they determined there really was some kind of neurological defect that was playing a part in the tendency toward stuttering. But there was nothing to do about that, and I had already mastered all the coping techniques that were available at the time, so it was time to move on with my life.
At my wedding, to a childhood friend and, coincidentally, a speech pathologist, I was so enamored seeing her float down the aisle that I was absolutely flawless with my speech.
After college, I started work for a telecommunications manufacturer -- pretty funny for a guy who was terrified of the telephone. But that job helped me deal with that fear. Now, the telephone holds no fear for me at all.
Now, I teach classes, lead teams, speak in front of large groups of people, sing, act -- it's all good. Sometimes there have been bobbles with the speech, but nothing that's significant. And yes, there has never, in my entire life, been any stuttering during singing or acting.
I admit it is a good feeling knowing that my four children would never suffer the speech related fears I did, though!