Outstanding post, K777angel!
Besides everything you described, another thing that makes me suspect Burke is that his red Swiss Army knife, the one LHP had hidden in the upstairs cupboard, was found near JonBenet's body. During the interview with the psychologist, Burke said "I know what happened." While describing what he'd supposedly been told that the killer did, he said the killer "took a knife." At the time of Burke's interview, no one, including John, Patsy and Burke, had been told that investigators had found Burke's knife, or any knife, near JonBenet's body.
If John and/or Patsy killed JonBenet and used the knife in any part of the crime or the staging, they must have forgotten to remove it from the crime scene...but why would they include it when telling Burke some concocted version of what happened to JonBenet? It doesn't make sense. I think Burke inadvertently took his sister's life and that the Swiss Army knife was somehow involved in what happened...but that John and Patsy didn't notice the knife when they staged the coverup.