The walk to her house would be in the opposite direction hence not bringing him back past the car. Walking there would probably be quicker than driving cos because it's actually a dead end - you can walk to where she is in seconds but not drive.
To drive her home you'd have turn back onto Cottingham and, initially driving away from her home, turn back into the road where she was sitting but further down. Which would mean she wouldn't necessarily have noticed he wasn't taking her home straight away.
I don't know where he'd go after that to get to the park. Whether via her street or not.
I agree with you about the offer of a warm lift or the claim to be a taxi driver. She must have been freezing by then, plus drunk. Very easily conned.
I also wonder if he employed a bit of assertive 'I know what's best' coercion rather than actual force which might have made her scream. Might explain anything that looked like uncertain, confused reluctance rather than struggling. That's just an opinion though
He'd already offended in her street which is very close to where he'd parked. His house is also minutes from where he'd parked but in the opposite direction. Straight through drive blocked by the dead end. Even though it's not a long detour but I'm still not in agreement with idea he'd seen her and parked.
There was no mention of his car at his sentencing. So I wonder did he park there on his way to a bit of offending once students started to return? Did he park there on the 20th before his Wellesley wank? Or did someone else see her and tell him to get there.