Just my theory... I don't peg JM as an intentional murderer... I mean, he has a job, and apartment, involvement in the community. My theory is that he gave her a mickey, it crashed her respiratory system that was already depressed b/c of alcohol or something that had been given to her earlier in the night (perhaps another mickey) and the drug killed her. I think JM may have intended to rape HG while she was under the influence, but I just don't peg him for being a guy who set out to kill someone. He doesn't seem angry-at-life or angry-at-people enough to be an intentional killer (based on the history that has been reported).
Once she died, he disposed of her.
If he did play a role in killing her (intentionally or unintentionally), I hope he is convicted and gets the full amount of jail. What a terrible loss for the world not to have a woman like HG in it.