BINGO! This wasn't just one crime. This was 1) breaking and entering, 2) kidnapping 3) child molestation and 4) murder. Before anyone blinks on the kidnapping part, I'm assuming that JBR was taken from either her bedroom or the kitchen by force to the basement.
All we really know now is that the guy is a perv. Where's his history of doing any of the other three things? And if he has none, why hasn't he done it in ten years since the murder of JBR when he's clearly had ample opportunities?
A total amateur at this, even if he's skilled at luring little girls into seclusion and exposing his wee-wee, is apt to cause several blunders commiting the other three crimes - particularly if he's never been to this house and doesn't even know his way around the neighborhood.
If Karr did it, I want him to fry but I see more holes in this scenario so far than I see answers. Maybe BPD will give us some answers but - at this point in time - I just don't see enough here to connect him.
Your points are well thought out.