I have the highest possible level of evidence: direct experience. It just happens to not be communicable. Not everything is.
> You can demonstrate that such a theatre might exist by demonstrating some phenomenon which cannot be accounted for via mechanistic processes.
All the mechanistic processes that you can account for where observed within the theater of your consciousness. So was everything you ever learned about science, and also this present discussion with me.
What I am pointing at is just Plato's Cave. Not a new argument, nor a settled one.