But the items used to dispose of her came from the house, so TH would've had to collect all those items beforehand and bring them to a car that wasn't his. It seems a little convoluted.
This isn't directed toward you, but I don't think there's any way he disposed of the tarp on foot or via a bicycle or anything like that. TH isn't in shape, and even though Alanna was small, 50 or so pounds of dead weight is very, very heavy. Also, someone would've seen him traveling that distance with a large tarp in his arms and/or strapped to a bicycle.
I think he either borrowed someone else's car, had an accomplice, or lied to someone about what was in the tarp (although this makes less sense to me, because why would anyone be okay with dumping a tarp like that in the middle of an intersection?).