Have a stutter too, I was in speech therapy from when I was 7, and one of the techniques that worked best was to focus on breathing and relaxation. When I blocked on words, the levels of tension in my body was/is extremely high. Specifically in my diaphragm, when there is tension, my chest is more rigid and the tension in mouth and tongue is so much stronger. So they had me focusing on relaxing my diaphragm which would allow the other tension to be less. So to focus on my breathing and being relaxed. (and yes I could sing fluidly, but my speech was very very blocky.)
The interesting thing was that this required thought and awareness, which is a bit difficult when you are younger. As I got older my confidence came, so became more relaxed in company and therefore less tense and so likely to stutter. I still do on occasion, but I am less concerned about it these days.