ITA. Whether Hailey met her demise in the living room or something happened there that caused her to leave or be removed from the house, the living room is key to me too. In addition to what you said, in the interview Shawn did with Priscilla Luong before he was named a suspect, she asked him what was going on when he came home on Monday 12/27. He says that Hailey was "just in the living room, watching tv". He goes on to state what Hailey told him she was going to her dad's and then to MB's to stay overnight. But, as BeanE pointed out a few days ago, his story just stops there. He doesn't say, "and then she just walked out the front/back door" or anything like that. Even in his account of that day (whether partially true or entirely fictional), Hailey never left the living room.
See parking lot, page 41, post 1023 for video. (Every time I try to post the link, the actual video posts...)