I have a story that has the unique problem of being so out there and so crazy that it's difficult for me to narrate it and sound believable. I think the answer is going to be to reproduce the story by saying "as told by" one of the cousins it happened to. This will change the timber of the collection but I think for it to come across as plausible that's really the only way.
The idea came to me while listening to Huckleberry Finn by Mark Twain. The accents done by the reader are perfect! Most people I've met don't realize there's a midwest accent but that's because unlike a little education and application can help you overcome it. Without those two things you tend to stay in the midwest and not come in contact with anyone who doesn't talk just like you do.