Thank you for sharing your experience =D My mother used to be religious and actually went through something very similar when her SP first began happening. The screeching is something that most people with SP do get. And once she went with it, it passed (not right away but). She is no longer a religious woman. I am not religious either nor do we believe in demons or anything of the like, lol. It is something that occurs when waking up during a certain sleep phase (when we REM sleep, our bodies are paralyzed; waking up during this stage will result in waking up paralyzed =/)
My mom has a very tough time sleeping because of the fear of this, her stress, and semi-irregular sleep cycles. Unfortunately, I don't think the SP will go away unless the above things are fixed.