Framing Miranda with murder actually does make sense, in a twisted way. If she simply brought the camera to the police while possessed, Doug would have solely been imprisoned. The video seen of Doug torturing Tracy would have only given evidence for torture, rather than murder, since Tracy was under the stairs. Even then, the imprisonment time could have been shorter than the actual sentence. Since such would not reveal Doug's acts of murder, the thought would not cross anybody's mind. He'd be a sexual predator, not a killer. This mindset would then leave him the perfect setup to go back and kill Miranda out of revenge once he satisfied the term of his parole. Doug had repressed his urges once before and it does not seem out of character for him to do so again to get revenge and continue "playing God." If Doug is murdered, any long-term threat to Miranda's life is out of the way.
Direct letters written towards Miranda could be used in a murder trial as an instance of her insanity. Since nobody believed Miranda's ghost stories initially, each letter could be viewed as Miranda's own writing. Minimal, ambiguous, on-the-spot communication could be seen by multiple people and (in spite of its presentation in cuts and blood) would not work in favor of an argument based around Miranda's alleged insanity.
"What's the score?"
"Dirty love." The Simpsons
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