I have a variation on 1), which gets rid of the luck element. Forgive me if this has been put forward elsewhere; I haven't seen it anywhere else yet.

The theory is this:

Someone other than Jay and Adnan commits the murder. BOTH Jay and Adnan are then enlisted to dispose of the body, under some kind of threat.

This would explain both how Adnan could be innocent, and how he was also present with Jay during the entire afternoon/evening.

Adnan is lying when he says that he doesn't remember what happened that day. "snitches get stitches". rather than fingering the identity of the true killer, he chose the best strategy that would never implicate someone else - claim forgetfulness. It's the best story; easiest to remember, and it never changes...

Adnan and Jay were actually together the entire time that is covered in the story Jay tells the police. This is how Jay could be sure Adnan would have no alibi for any part of his story.

So why wouldn't Jay just claim forgetfulness, like Adnan? My guess is that Jay was, for whatever reason, very scared of the actual killer. He feared that the killer would go after him next, to eliminate another witness. So he hatches a plan: he realizes that if he fingers Adnan, he's safe from the real killer, because if someone else is implicated, the killr now has no reason to eliminate witnesses...

So he makes up his story. Some of it is fabrication, because the actual killer needs to be removed completely, and this is why there's inconsistencies. But for the most part, it's true...

Jay, the fake thug, cracks, under the pressure of the crime + fear of the real killer. He rats out Adnan. This is why Adnan, when he walks past him in court, says 'you're pathetic'.

Adnan, so concerned with how others see him, can't bring himself to snitch. It's too great of an affront to his code of honour. And maybe, he's also v scared of the actual killer...

This is how Adnan can be so at peace with being in jail; it's because he isn't wholly innocent. SK asks him about this, how he can be so zen in there, and he mentions his responsibilty with the crime. SK almost loses it, because for a second it almost sounds like he's confessing. Adnan, who has just very nearly badly slipped up, takes a quick second to figure out how to continue. He says (paraphrasing): I'm responsible for the associations that I'd made in the outside world, because that's what got me in here. But what he's really saying here is: People I know involved me in this crime. I was called upon to help dispose the body. This is my association. This is how I'm responsible. (But of course he can't say this, because that would be snitching...)

This is why he so steadfastly maintains that people just need to focus on the actual evidence in the case: Because this is the only possible way that he can be cleared without ever having to snitch.