Starting with the assumption that spidercam shows him and Libby (which is a very good assumption for reasons that have been detailed here on numerous occasions) and that he gave his sister the strange tale that connects him to her physically within the relevant time frame (his claims of pushing her away) then I'd struggle to think of a reasonable version.
If he'd claimed to be working as a taxi driver or even just to be helping a distressed girl as his sister suggests - he would have dropped her somewhere safe or even unsafe and left. The dropping off part is conspicuously absent from his sisters account.
He'd have shown up on CCTV somewhere at a time that would be helpful to him and that would match his version. She probably would have been seen as well if dropped somewhere. She'd probably have got home somehow.
The police searches focused very quickly on the park. I would imagine that something concrete led them there - be it CCTV or dashcam or witness statements. That is not somewhere safe. After his arrest they searched a bench.
As you say - there is no good reason to go to a freezing cold, isolated park with a very vulnerable girl.
The time frame police seem interested in is 11pm to 3am. That's the period they requested info for - including the Croda CCTV which is close to that park. It's reasonable to assume there are reasons for that. So is it possible that CCTV footage doesn't show his car leaving the parks vicinity till around that time?
Spidercam is 12.10. That's a depressingly long time frame for a reasonable version.
So surely all reasonable versions start to fall down with the park and the time. As
@Cherwell has pointed out she was not capable of consenting to anything should he have claimed that is why he went there. I can see no other reason to go there.
If he admits to rape (even if just by trying to claim consent) and then to leaving her there - she would have to have fallen prey to another predator. In a freezing cold, isolated park. Surely the probabilities of that are tiny
So the only versions I can think of where he could reasonably claim to leaving her after an inordinately long time are that that somehow she died of natural causes or she was attacked by someone else. Neither seem reasonable.
I hope he pleads guilty. Her loved ones shouldn't have to live through any more.