It isn't plausible that JR committed this crime. Patsy wrote the note, and if JDI then she decided to cover up for John - and I think this is a fantastical idea. JDI theorists believe that Patsy would cover for John in order to maintain her status and her lifestyle. But, Patsy would have done great during a divorce, getting half of John's considerable assets plus child/spousal support.
Patsy did the crime (a rage/accident killing IMO), and John felt compelled to cover for Patsy because Patsy "had something" on John (she knew about the molesting, and she was always a risk to reveal this molesting if John ever dared think about telling the police the truth about Patsy doing the crime).
JDI is more plausible than IDI, but that isn't saying much. If I could break down a percentage of likelihood, it would be 90% PDI, 9% BDI and .99% JDI and .01% IDI The odds that John did it are very slim, but the odds of an intruder doing it are absolutely astronomical.
I can't rule Burke out completely - but he was 9 years old and has been very well-adjusted after this crime. I actually think Burke thinks his parents are innocent of any wrongdoing and that it really was an intruder. If Burke thought his parents did this, I can imagine him being more than willing to talk about it, especially since so many out there suspect him of doing the crime. In this case an innocent Burke who believes his parents (one, the other or both) killed his sister would be at some level angry that there are those calling him a killer. He'd talk.
It is plausible that JR was involved in the murder. I agree that PR wrote the RN. I also agree that PR would not cover up for JR.
If the murderer was PR, then PR did not need to have something on him for JR to want to cover for her. I believe JR would have covered for her anyway because he loved her and he felt empathy toward her.
Have you considered this scenario: PR does the head bash and JR the strangulation?
I believe BR knows exactly what happened to his sister, whether he was involved in the murder or not. I think BR was glad his sister was gone because now he could start getting some of the attention piled on her. I don't think BR loved his sister. IMO his lack of emotion regarding her was very revealing in that regard, but this does not indicate BR killed his sister. It indicates BR has some issues that are outside of normal.