I'm not as well read as most of you, I think, but I have read the bible so I do see the Eden allusion. But although I can see it there, I don't have to then take the story as a retelling of the Eden story, or to dismiss parts of the story that don't fit with that. The Eden story has a moral slant which seems rather odd in the context of BBM. It's about the start of sin, if I remember correctly - there's a powerful, watchful, vengeful God/father figure who is clearly in the right (he's God), and Adam and Eve (and therefore the rest of humanity) are clearly in the wrong. Obviously, this doesn't translate to BBM, unless we were to believe that Jack and Ennis really WERE wrong (or that homosexuality is wrong, or giving in to that temptation is wrong).
So it always seems to me that the Eden stuff is to do with Ennis. He's the one who believes they are 'innocent' and that nothing is wrong (not Jack, who has a different take on the events of the summer), until he gets the 'knowledge' that it's wrong and feels shame. He's the one who feel like he's falling, not Jack. And it's pretty easy to fit that father figure in there too, especially if applying it to Ennis.
So to me, the Eden reference isn't telling us that this it the Eden story - it's maybe just giving us an extra insight into what's going on with Ennis (almost the whole story is from his point of view, really). And it could very well be the same with the idyll thing - it tells us a little about what's going on for Ennis - that pastoral innocence, but isn't meant to make us discount parts of the story (such as Jack's view).
(No offence intended to Judeo-Christian believers - this is just my non-religious take on the Eden story).