I've been following this case since the day Jessica went missing. I have merely lurked on all of these threads until now, primarily because I've been waiting until I feel I have something worthwhile to contribute to the discussion. You guys have definitely covered most, if not all, of the aspects of this case, and I have read many plausible and well thought out theories. I will try to keep my thoughts as short as possible.
This case has kept me up for several nights now, just wondering WHO was so sick and pathetic to have done this. Statistically speaking, it is a white male. In my personal opinion, it is either a bona fide serial killer (organized), who has the experience and drive to evade the FBI and the police, because he wants to continue his sick career (I think these types of killers pride themselves on how well they do their "job" ... examples, BTK, Bundy ... experimenting with the variables of the crime, learning from their past mistakes, etc)
OR I think it could be a man who has a history of sex offenses, probably of a violent nature, or has committed petty crimes. However he has never murdered until now. Think John Gardener. He may have had some sort of mental breakdown (for lack of a better term) before or while committing the crime, hence the terrible nature and extreme amount of violence. This breakdown could have come on by life events such as divorce or ending a relationship, getting fired from a job, caught violating parole, etc.
But, even though it was impulsive, like Gardener he won't be able to stop now that he has killed.
For the organized killer I described, I think it will be someone who has a job or position in the community where he is managing/in control of others OR working with children, the mental health profession, even volunteering with the disadvantaged. He may even be a doctor, considering that poor child was dismembered, I'm not sure how much knowledge of anatomy that would require. Remember, BTK worked in security, and Bundy at one point was taking suicide hotline calls. My point is, this type of killer will get off on pretending to "help" others, being the wolf in sheeps clothing - he may be a teacher, counselor, psychologist. He may work in law enforcement or security. This person lives alone or with a wife, maybe even kids. He wears a mask of normalcy and that is why he alludes police so well. He is accepted by society and raises no red flags. It really freaks me out that this person might very well be law enforcement ... maybe in a different jurisdiction?
The disorganized killer may still live with family, or be dependent on family financially. If he has a job, it is not rewarding work ... general labor or entry level. He will blame the world for his problems. If he has any history of opposite sex relationships, they will be short lived, maybe violent. I think Brandon Lavergne fits this type, too.
As for if this person is a pedophile, it's my personal opinion that this guy may have adult victims as well. To psychopaths that hate women (which I think this monster obviously does), age isn't as big of a consideration as gender and opportunity. I'm reminded of Polly Klaas' killer who said, "I didn't kill that little broad". They don't see what we see - a child, a teenager, a woman ... they only see a representation of what is female, what they want to take their sick and twisted rage out on.
ETA: Hopefully the FBI has enough evidence to be able to do a lot of profiling work on this guy.
I hope this post wasn't too long, I'm looking forward to reading your replies.