I do not have a solution to offer, but wanted to give you a bit of info. In grad school, when we discussed stuttering/fluency, my professor stated that words that carry more linguistic weight (more significance) tend to be stuttered. For instance, someone will more likely stutter when telling someone their name, friend/family’s name, their job title, etc. This doesn’t particular help in terms of neutralizing it or anything, but I thought it was interesting and thought it might provide some insight or peace of mind.