Sorry if I'm repeating/rehashing anything here. Every now and again, I need to get my head back into what is actually known about the case, and think about what that tells us about the killer.
----Elizabeth was missing for several days prior to her body being found.
--- Her body was drained of blood and washed clean, somewhere other than the discovery site.
--- There is evidence that Elizabeth was tortured for some time prior to her death.
-- Her body was transported to the discovery site. We must assume by wheeled vehicle - car, pickup, van.
This all tells me:
-- The killer had access to private space in a building with running water, for at least a week.
-- The actual crime scene was somewhere secure to the killer, somewhere he could keep and torture his victim and then deal with her remains, without interruption.
-- The kill site was somewhere her screams would go unheard.
-- The killer had access to a vehicle.
-- The killer could load Elizabeth's body into this vehicle without being seen.
Looking at her body and taking into account the parcel sent to police containing her personal effects:
-- The killer was quite comfortable with depraved and cruel acts of torture and dismemberment. Not many people are. This guy was, completely, comfortable with it.
-- This was not a sudden, frenzied crime -- everything about it seems very controlled.
-- The killer took great care with details in the posing. They had some significance to him, or he'd not have taken the time/risk.
-- The killer was invested in profoundly humiliating his victim.
-- The killer was proud of his work, he felt powerful and secure enough to taunt police. Possibly, he was attempting to divert attention from himself, though.
^ And all this is why I tend to tend to think her killer was not living a life of transient poverty in seedy hotels.
This all suggests free access to a privately owned, secure site -- the killer was not at all interrupted through the entire, horrendous and bloody murder, and subsequent washing of the body, let alone whatever he did to her in the days prior to her death. He had running water, too, which derelict buildings often do not have. So, logically, it is more likely to be a private work or living space, in which the killer felt secure enough to keep and torture and kill his victim. He had expectations of privacy there. This was his kingdom, so to speak. I think it's probably his own home unless he had some kind of work space that no-one else visited and/or which he could easily close down for a few days.
-- Elizabeth's body was the direct opposite of 'concealed' - it was carefully and deliberately posed in an open area surrounded by occupied homes.
-- The killer felt secure enough to take the time to not only remove her body from his vehicle at this location, but spend some time with the body at the site as well, enough to commit multiple acts of posing.
^ This suggests to me:
-- That the killer was heavily invested in the body being found and seen in its humiliating, shocking state. He was making a point, here.
-- The killer likely parked very close by.
-- The killer very likely either knew the area and the habits of the people in it, or scoped it out prior to the dumping of the body. He needed somewhere he could make his point, in a publicly accessible place, where he could feel secure in taking the necessary time with the body.
I don't think this killer was down at heel, living in cheap rented places. I think he had a home and a vehicle and felt secure in using them for this crime. I don't think he was seriously delusional, there's too much control shown. I think he was a stone cold sociopath, one who was comfortable with torture and mutilation and handling body parts to boot, comfortable in humiliating his victim even after her death. While he might have a superficially charming exterior as many sociopaths do, in this case I highly doubt anyone close to him, knowing him for an extended period like family members, old school pals, workmates, would remain wholly oblivious to the truth of his nature. He was either an utter loner, living away from family -- or he wasn't, so there could be people who not only know he's a sociopath, but noticed absences and other telling behaviours around that time.
While it's tempting to assume there must be other crimes, and think of him a serial killer (which would increase the chance of him being identified, eventually) this really could have been his one and only, a fantasy played out that he could enjoy for many years to come thanks to the media furore, which he well and truly fuelled. Though I very highly doubt it was his only act of violence and cruelty against women.
Just touching base. Again, sorry if it's all been said before.