I have quite a stuttering story but there is a doctor who has all the answers. I have an appointment with him in 10 days. He's world-renowned as the expert. If you Google him you’ll think so too. Stuttering is multi-faceted as you have explained, but physiology plays a large role. This doctor successfully uses medication to treat stuttering. Lookup Dr. Gerald Maguire, MD. He is doing cutting-edge research and has a clinical trial at the NIH. This is the study reference https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7118465/