Even though there are people who did overcome their stutter, a lot of the stories we hear are about people who either had VERY mild stutters or just actually spoke very fast. Speech impediments come in many shapes and forms. I'm in a very similar situation as you. I stutter with everyone even though I don't care about it, or so I believe. I also stutter when reading Quran but to a lesser extent. Success stories from other people should motivate us to overcome our stutters. We might not do it as fast as they did, or in the same way they did, but I try to focus more on the "that means it's doable" part.