I think he beat and drugged her during the 5 minute parking lot stop. Then, once he had her drugged he was going to do whatever he wanted. Killing her at the abandoned house was because there was no way he could let her live.
He must have been raging and on the edge of doing something like this. He was a creeper in the neighborhood-- people saw he was a user and manipulator who didn't like being told "no" by the people he creeped out. He knew that he was going to go to prison for the theft. He had to have known they knew it was him-- I would not be surprised if he was spoken to that night at work or saw them investigating the theft. At that point, what did he have to lose, he was going to prison and probably was very angry.
He was probably looking for someone to victimize -- and that she appeared to be someone who had it all-- not as an heiress but could be as fit as she was, jogging at 4:30 am with all of the other people who can afford to do that--- she became a quick and immediate target.
I am so sorry for her and her family. To have her ripped from them is awful. To know she was beaten so badly and drugged is beyond belief. And, the final insult was to have her out in the open with all of the decaying and decomposition is abhorrent.