I‘ve got exactly the same problem.. I think there are some factors contributing to more stuttering when telling a story. Firstly, telling a longer story is a more difficult task for your brain than just saying some meaningless words. Secondly, when starting to tell a longer story the expectations of the listeners are higher, which causes more stress for the person telling it, resulting in more stuttering for a stutterer. When I‘m with my friends I also avoid telling longer stories, so I always try to tell something as short as possible to avoid stuttering. I‘m currently trying to be more open about that with my friends tho, so I think talking to them about it can really help because you won‘t have to avoid stuttering that much anymore. I hope my answer makes sense :)