Why couldn't the strangulation be part of a sex game? Not all strangulation sex games are meant to end in death. How about JR strangling her and getting off watching her struggle a bit, then when he lets up she screams, he picks up something and bashes her head to shut her up, then goes ahead and kills her by strangling her to ensure she never could tell anybody about their games. Nobody would have to stop to stage anything about the death, they just would have to stage the coverup.
Well, there are people who have outlined that theory.