Ok, Theory
a-hole is out and his truck breaks down. He calls Liana to come get him. She stops for gas or waves to a neighbor on her way (midnight witness). She picks him up. It is late, she is tired, maybe he was drinking or whatever. They argue and he hits her, killing her. He panics, carries her body to where she was found and drives her vehicle home. At home he is panicking. He needs an alibi. So he drives her vehicle to where it was found and stages what he thinks will look like a struggle. He then walks home and waits for a call about her not showing up for work. Instead, the witnesses start calling police first, re: the vehicle. He had already thought of his alibi- he was asleep when she left. So when police call, he gives him the rehearsed alibi, not knowing what time the witnesses called about the vehicle.
That would explain the second degree charge, as the murder occurred in the heat of the moment (during the argument). Indignty to a body was probably because he undressed her, if she was found in street wear, that would kill his alibi that she left for work as normal. He may not have thought that LE would notice a beatup old truck near the scene, as long as it wasn't right at the scene. Or maybe he was trying to think of a way to go back and get it, while they were searching for her- but didn't have a chance.