He didn't jog to the store at 1:30. The store videotape shows him going out to her car. It's likely that either he had just dumped her somewhere, or her body was in the car, and he was about to dump her. But he needed a smoke.
I didn't see her car in the video. Nor did I hear anyone point this out.
If that's the case, then he'd most likely dumped her body in the dumpster behind the apt. complex. He was on his way to plant her car at the park.
He hadn't washed his hands, hence the blood smears/stains inside her car.