Regarding speaking more easily/fluently when alone, that's a great question and it's long been known to be the experience of many people who stutter, though it's certainly not universal. One of my friends stutters a lot with her cat! There is research ongoing, Dr. Eric Jackson is looking at this but I would hypothesize that general observation in terms of attentional/cognitive load. Speaking/formulating language isn't necessarily (or ever?) an automatic process in people who stutter, so when those higher attentional networks are engaged in other things, I think the likelihood of moments of stuttering increases. Regarding psychedelic treatments, I know of no research in this area. BUT, I would strongly agree that the experience of living with stuttering functions much like PTSD in that relieving speaking is much like episodes of PTSD regarding speech/communication difficulties.