Prepping behavioral answers with the STAR method and I sound like a corporate robot

I've got a round of behavioral interviews coming up and everyone says use STAR, Situation, Task, Action, Result. When I write my answers out that way they're complete but they read like a performance review, not a person talking.

How do you keep the structure without killing the honesty? Do you memorize bullet points, or just the stories and let the actual words come out live?