Who says he was desperate? If he was in fact someone known to the family, especially if a teen or college age guy, he had a lot of options: give it up, claim Elizabeth had begged him to sneak out together because she needed to talk,let her go and run for it while everyone's attention was on her, hide and keep Elizabeth quiet with a gun to her head, etc. And if I was out in a wooded area in a suburban neighborhood, with a girl I'd just kidnapped, and heard the voices of 40-50 searchers in the immediate area, I sure wouldn't assume they were all unarmed. I'd have been packing my .357 Magnum if I'd been searching in a situation like that, and I'll bet a number of the searchers were well-armed. Heck, the police were probably happy to have the back-up.
Why would anyone possibly think that Liz and the alleged perpetrator would still be lolling around the neighborhood 2 to 3 hours after the deed was done? Makes no sense at all. It looks more and more like the "big search" was a big CYA.
Well, let me see.....we've been told that he issued threats of harm to MK/Elizabeth/the family (depending on which version you adhere to)......sounds pretty desperate to me. In any event, I still can't see the police allowing citizens to roam about with an armed gunman and his hostage on the loose. It just doesn't sound safe for anyone involved.