Another thought on this: Why not stage the scene as an accidental fall instead of a kidnapping? Because the body was strangled with the garrote. This is literally the only reason that the ransom note exists. It's because the R's knew that while the police/M.E. might buy an accidental fall, there's absolute no way to explain the strangling marks. If BR did it and the R's both cover to save him, they would have to explain the scene in a way that makes sense. The garotte and other marks on the body had to be explained in an alternative way and thus the RN & phony kidnapping. I honestly think it's that simple.