The therapy in college’s Speech and Hearing Center centered around this. The theory is elongate the initial sound of a word to ease into it. Then repeat the technique on every other word (to get a “flow” going) or when you sense a block coming. As you get into the flow of the speaking pattern, you’ll need to use it on fewer words. Easing into a sound minimizes the chance of a block, and it as a secondary effect of slowing your speech down (and speaking more slowly usually helps fluency). The technique works, and I’m still using it 25 years later. Is it perceptible to listeners? Maybe. But it’s definitely LESS noticeable than struggling through a hard block.