When do you think he would have rented it? The day she went missing, the night before? I don't see him spending the $ on this for such a short time. What does Pa$tor Tim drive? Jk, kind of..
I think it was early that day and the station story is from when the van rented from the airport switch took place. He may have been thinking about what really happened as he lied, it seems to me. And then 'she departed...' in that nice shiny rented mini-van from the airport with the accomplice/him. My guess would be he dropped somebody off, but drove the car back himself, and he felt like he got away with it when he drove the car back, thus "she departed." The wistful words he saw as he was driving around disposing of AJ's body and thought about.