I am a lot better now than I was as a child, but I used to be a master at the art of avoidance and replacement. If I felt I was going to stutter on a given word, I'd replace it with something I felt more confident with. I was constantly evading a ruthless, arbitrary censor, and I'm certain it gave me a greater facility with synonyms, rephrasing, and general linguistic flexibility. I have a natural talent there, but the stutter and my work-arounds made me hone it to a level most people never have to.
I had to preempt the word and then either imagine a synonym or add a long vowel as a launching pad ...."Oh! Blackboard"
What really worked for me was to force myself to _never_ replace words and to accept that I will stutter at times.
I also have a silly trick for overcoming a prolongation. When I'm stuck, I voice the first sound of the word, then take a short silent rest, and continue with the rest of the word. For instance, "f...ailure". Knowing that I can plough through any prolongation and still be understood has reduced them tremendously and lowered my anxiety. I'm not saying this trick will work for everyone, and I haven't seen it in any of the books.
Unlike the author, I think there's nothing wrong with apologizing for a stutter. That's a useful tactic because it brings the issue out in the open, instead of putting all that effort into hiding it. I'll apologize in advance, just to lower my stress level.
Edit: Renamed block to prolongation.
Completely agree that there's nothing wrong with apologizing for it. It lays it all out instead the other party wondering why you are nervous, or think you are hiding something. Finding the appropriate time to bring it up has always been a challenge. I sometimes will do a fake stutter, and bring it up after that so I have more control of the situation.
When I am forced to speak to a room full of people it's usually spur of the moment. If I know exactly what I'm talking about, I tend to talk too fast. When I'm unsure of myself or how to phrase things, my stuttering is almost completely debilitating even when I'm controlling my rate of speech. I figure alcohol could help in both situations by keeping me relaxed and more focused.
I've stuttered all my life and still do, far less noticeably now. I've largely overcome it through mental will and practice. Speech therapy teaches you a bunch of tricks and techniques, practice and repetition eventually makes them second-nature. For me, it mostly came to becoming aware what your body is doing during a block -- you're always aware you're having a block, it's harder to notice the tension in specific muscles. Once you learn to recognize it, you can back off for a sec, let the tension dissipate, then approach it again. It's a terribly slow impatient process at first, but just like any skill, you practice it and you get better at it. Eventually you float in and out of Flow state.
It's definitely changed me... like any skill you practice, it makes you far more disciplined. I feel I'm more patient. I do have scars, and it does sometimes come back, but if I was able to largely overcome that through mental effort and determination, a lot of other things feel far less daunting. Builds a sense of resiliency and gumption.
But back to alcohol, it's not just your physical skills that get sloppy, it's your mental skills too. I'll go out for a social drink, but sloppy drunk is reserved only for kareoke. The it-doesn't-happen-while-singing bit is true.
I do not stutter; I find that alcohol distorts control and introduces uncertainty - for me it is the opposite of liquid confidence. Alcohol helps to relax, its great for social settings where I can be overly analytic or speak with too much force, but in a debate or speech setting the clarity of mind lets me bring all my faculties to bear.
So in short, I don't find that relaxed and focused is an effect, just relaxed. If that helps with your stuttering then go for it