Thanks for the video! 2:27 shows the process. They go letter by letter in order and then ask yes or no. I think asking about the next letter based on previous letters would vastly improved the speed
The downside is that with a powerful enough model you could replace the patient with a coinflip and have a hard time telling the difference.
I think that may already do what you want?
A basic markov chain predictor seems like it could work, if you had a short enough window to be sure it couldn't invent its own nonsense.