We have to bear in mind that there was no screaming between 12:14 and at least 12:15, but then the screaming started. I know the witness could have been woken by screaming and not registered what had woken him up, but my point is that if he'd carried Libby from the car to the river the screaming that was heard started over 4 minutes later. That minute of quietness between 12:14-12:15 ,and possibly from 12:11 to 12:14, suggests to me that there could have been a period where she was trying to be quiet, hiding. I think she'd have been screaming continuously if he was carrying her all the way through the park to the water's edge.
Perhaps he did rape her near the car and she was too petrified to scream. Then as he's picked her up (12:15) and carried her to the river she's started screaming and screams constantly until he gets her to the water's edge. He needs to have left the river to get back to the car at a fast walk I'd guess at about 12:17, so with her ability to scream between 12:15 and 12:17 (I'm ignoring the 4 - 7 minutes of screaming reported) would he have put her down to 'gently' asphyxiate her at the water's edge before making his escape?
There are too many unknown variables in my scenarios but we have to be guided I think by what the witness with the phone heard and didn't hear, to try to eliminate some scenarios. The minute of silence before screams is most puzzling, perhaps that was during the rape while Libby is using her energy not to scream but to fight and scratch him. But that suggests she got into the park under her own steam, which would have been at a slower more staggered pace, and it also suggests he didn't asphyxiate her during the rape, because she could scream afterwards.