My girlfriend stutters and experiences this as well. We looked into it at one point and I believe that the brain uses different pathways for reflexive speech vs. "imitative speech." It's the same if she speaks in a sing-songy manner or sings. We also had a family friend who suffered a stroke and could no longer speak... yet he would come over for Christmas and could sing carols like an angel. Different pathways. My gf has a Russian character that she does can speak flawlessly. But I don't think you could suddenly become someone else unless you moved to a different town. She doesn't practice this, but her old speech therapist recommended speaking slowly and deliberately in a song-songy way. I obviously can't put this into practice myself, but I always wondered if you just put some different affectations on your words if it would help a stutterer get through sentences.