I've thought all the same things as you just expressed here.
But one thing always bugs me -- the nature of the coverup. Assume the garrote and genital trauma were coverup, it would a pretty 'determined' person to do that. It's one thing to lie but to then actually interject yourself into the crime in such a horrific manner and strangle your daughter's neck, probe her genitls etc. I always struggle with that.
Yet, I can totally buy the parent(s) wanting to cover for a kid. It's such a paradox.
Obviously the parent(s) felt they couldn't go to the police for whatever reason. Say the head injury came first and it was an accident why not call the police? Perhaps Patsy hit JonBenet accidentally killing her but knew she couldn't go to the police because she was aware JonBenet was being molested? Maybe she was the molester? Maybe she allowed or knew someone else was. Maybe that's what prevented her from calling 911 if the accidental head injury thing happened first. The fact that dirty secrets would be expressed. The head injury trapped her into the lie. Or to go with your line of thinking -- Burke's actions trapped them into a lie.
Assuming the garrote and genital trauma to be cover-ups may be the reason for your difficulty in seeing how this may have happened, causing the Rs to inject themselves into the crime. Indeed, I think its the biggest reason investigators havent been able to see it for what it was.
Consider for a moment that what the parents were confronted with in the middle of the night was a sexually assaulted child who had been accidentally killed by strangulation. The appearance of everything that happened pointed to the person responsible. In order to save that person (and their own public image), they had to alter the appearance of everything to make it look like something else -- and make it look like anyone else did it, even if it meant throwing their own friends/acquaintances/employees/business associates under the proverbial bus.
The RN they invented didnt work very well -- the FBI saw through that immediately. But it did throw off the BPD long enough to have them treated like victims instead of suspects. It is probably the main reason they were allowed to leave the house without being searched for evidence or taken into custody for questioning.
But the garrote: Oh, that worked like a charm. I have to give credit to JR for a brilliant idea. I think its obvious that its not real, but almost everyone tries to figure out how it might have been used because they cant get past the fact that it was found attached to her neck. Even though it isnt anything like a real garrote, and it wouldnt functionally work very well for the purpose its presence implies, no one can get past realizing it wasnt used as it was found on JonBenets neck. It was altered to make it appear to be something else entirely because, if investigators knew what really happened, their first suspect would probably be the one the parents were covering for.
And as for the sexual injuries, dont fall for the incorrect (IMO) assumption they were inflicted to hide something else. That logic is flawed simply because of the evidence of an attempt to erase that aspect of what happened.
One other thing to consider,
LFB: What if the parents didnt even know about the head blow? There were no visual signs of it. Even the coroner was unaware of it until he peeled back her scalp and saw the blood and the cracked skull. The parents may very well have only known about the obvious signs of the recent sexual assault and the accidental strangulation. Perhaps they thought they could hide the evidence of the sexual part and it wouldnt be discovered; and the accidental strangulation was altered to make it appear to be intentional.