I’m currently an aspiring voice actor with a stutter and what really helps me stay fluent is simply changing my voice; whether it be the tone, accent, inflections on specific words or sounds, the volume of my speech, the pitch of it, etc. My advice for fluency to just experiment and find aspects like that which are able to click with you. As for the anxiety, my best advice for that is to stop seeing the role as a separate thing you need to fill. Rather, see yourself as the character and get in their mindset. Basically kind of like the whole “fake it till you make it” strategy except in the case of acting that’s the whole point.