I would play in loud music in my headphones when I'm going to read something to lessen the probability of me stuttering, or better, record myself reading smoothly so I could easily follow along (i dont think this would work with you since you have to portray emotions reading the script and whatnot). A little backstory, I'm 21 years old and a few months ago I had this online thesis defense on zoom, just like you I can read the things I'm going to say smoothly at one point, then moments later not beinf able to read smoothly at all. Music really helps. You can do this! From my experience, people tend to be more understanding than we think. :))