There's still a part of me thinking they are searching in the wrong area, here's another scenario,
He picks her up and drives to the park, CCTV picks him up entering the park with her in the passenger seat,when he leaves they only see him in the car so police assume she must be somewhere in the park area, be it river, pond, bushes....
But what if the screaming that was heard was him forcing her into the boot of the car, I doubt she would have got in there without a fight, then someone said they heard a bang, like a gate closing..maybe this was him slamming the boot shut.
I know this is unlikely but it's a thought, he maybe knows the park and knows its likely empty at that time of night,
he couldn't do anything on Haworth street as it's far to close to properties and busy roads.