Your theory is based on two faulty premises:
1. that JW's alibi rests on not being able to reach LS. In fact, JW never tried to reach LS that night, as you say. Rather, his story is that she was supposed to contact him, but never did. He only tried to contact her the next day. His alibi also rests on the assertion by his roommate(s?), which have been given to the FBI, that he never left home. If his roommate lied, he could receive a penalty of 5 years in prison and or a $250,000 fine for making false statements to the federal government.
2. that "everyone" was watching the game. In fact, the supposed purpose of going to JR's was to watch the game. As you've noted, the game was over before they arrived at JR's, but while it's entirely possible that the game claim was to cover the true purpose of going there - to do drugs - they might well have intended to watch it via DVR.
You also ignore the assertion of an apparently in the know PT poster that the family has said they don't believe JW is involved. If you choose not to believe that, however, I believe your theory is illogical. If there were calls between LS and JW, that would be clear from both of their phones. LE has LS's phone, and presumably can easily recover anything that might be deleted from it (assuming it can be deleted in the first place), as well as any prints on the phone. They also likely have access to JW's phone - they've described him as cooperative and searched his house. Given that they can tell from the phones about contact between the two, why would CS have to say something publicly that contradicts his story (and what would be the benefit of doing so)?
As for my theory about the 12:16 call, it's simple. She called JR and/or DR (if they were not together already) to arrange to go with DR to JR's around 12:30. Occam's razor. While there certainly may have been another motive for CS's statement, which I have theorized relates to drug use, its express purpose had nothing to do with the case: "The purpose of what I am sharing with you is not to speculate about what happened. The purpose of this is to encourage people to take precautions to be safe."