Okay. I prefer "hard" things such as dna and fingerprints to the more "soft" stuff that is reminiscent of tea leaves such as trying to discern the character of the perpetrator.
However, there is not much hard evidence and we don't have access to the dna of the various 'suspects' that have been discussed so far.

So is it a "Demented Creep" that was playing games with a six year old girl? What would we be looking for?

Age? Prime age for that sort of stuff is low twenties.
Personality? Loner. And lonely. Socially awkward in his actions and in his understanding. Perhaps he has to deal with an actual impediment such as a tendancy to stutter particularly when he is in a social situation. Or perhaps instead of an actual stammer he simply is very uncomfortable in a social situation, particularly one involving a female of his own age group.
Theory of Mind? Probably self centered and not as able to relate to someone else's view point very well. Perhaps he even lies somewhere along that famed "Autistic Spectrum"? If so, those who see him as bright would perhaps term him 'Asperger's Syndrome' a category of considerable 'bandwagon' status these days but one that does have some sort of actual existence and might be significant in this case.

Habitus? Probably Klinefelters or marginally so in his appearance. Tall, thin, somewhat female in his physical appearance. Long legs. If so, this would most likely render him having very little muscular development and very little strength in what muscles he did have. So perhaps I have been wrong in viewing the garotte as a means to exercise precise control over the strangulation. Perhaps the garotte should be viewed as his only way to strangle someone because his grip strength is indeed in lowest ranges. He may not have used the garotte so as to experience the exquisite joy of a slowly strangled victim, he may just have needed "an assistive device" in order to accomplish the task at all. He is probably a male who actually has a "husband" in his kitchen cabinet! ("husband" is a woman's term for the ribbed-rubberized glove-type devices used to provide a better grip for opening recalcitrant jars).

Neurology? Probably a minor problem with prefrontal lobes. More a history of a few epileptic episodes rather than a full-blown problem. He would probably have a very acute appreciation of music, though not necessarily loud music. I doubt he would be a musician due to his lack of manual dexterity and coordination in his movements. His lack of fine motor control would prevent his playing an instrument and his lack of social skills would prevent him from ever learning one, but he could well have a passionate interest in music since his brain experiences it so differently than most people do. he would also have turned to music quite early in life, probably before his teenage years. Even though his body would be low in testosterone, his brain would have been fairly high in response to pre-natal testosterone. So he would be a 'somewhat masculine brain imprisoned in a rather feminized body'.

Employment? Well, thats a bit more difficult to speculate about. Surely he would need something not too demanding of social skills so he would turn to something highly technical and would probably be very good at it. So perhaps that is why he can afford all those true crime books and true crime/action/adventure videos. He makes good money as a computer programmer. He can administer systems. He can't administer people though! And eventually his co-workers realize this and lose all respect for him. And his employment while highly remunerative is probably rather punctuated with bouts of unemployment. He probably gets most jobs from temporary agencies that farm out computer programmers, so he doesn't really have to deal with interviews because he would not do well in them.

Interests: Probably rather wide ranging but primarily focused on a few items. Music, computers, probably true crime. He is not dumb intellectually, just socially. He could buy a book on any subject at all, but he couldn't carry on a conversation about it too well and probably not at all with a female.

Did Access Graphics ever hire a temporary programmer who utterly lacked social skills but who saw JonBenet being brought to the office some day?