When you change your voice you are acting, and some people don't stutter when acting. It is the same reason why we don't stutter when we sing: we use the brain differently. ​ I have used a similar technique that I have developed over the years, and I don't stutter normally. However, I still have a stammer, which means that I spend time and effort every time I speak, making my speech somewhat slower and often a bit 'confused'. That's a trade-off I am willing to make. At least for now. So, I think you're on the right path. You can't cure it, but you can control it.