This earlier post you made has bearing on your recent post since you repeatedly characterize the circumstances by assuming an intruder. For example, I don't assume the note writer was the killer, but your posts assume both that and an intruder. By projecting bias backwards to characterize the evidence, you commit the logical flaw of "begging the question."
This is clear in the 4 points you cited above as attributes suggesting a hard core career criminal as intruder/killer. These points are flawed as follows:
1. A "hard core career criminal" (HCCC) would have no reason to do anything but use his hands to immediately silence and strangle a small child if he came to kill. There's no need to a HCCC for a garrote or to leave it as evidence. Fiddling with a rope gives time to scream...and why would a HCCC care more about shedding a child's blood than, say, a parent would? If a HCCC came to kill, a note seems unlikely, but even if written, why leave evidence if he unexpectedly killed her?
2. Use of "headbash"? Would an HCCC intruder or someone close to the child have a greater stake in making sure she did not survive to identify him/her? Sorry, no HCCC advantage over family. Overkill suggests someone close. Strike ll.
3. Use of ransom note? Your supposed "HCCC" writes a lengthy note for ransom which he leaves as evidence, but then forgets to take the victim? OK, maybe so, but who as killers would have a greater need to suggest an alternative scenario, family or intruder? Stated another way, would someone who can quietly slip away in the night be as likely to try to put a spin on events as someone who has to stay in the house and explain things? Sorry, no presumption for a HCCC kidnapper who leaves the victim and evidence he could take with him.
4. You think comments from movies with violent themes in the note suggest a hard core career criminal? What about a kid, teenager, or anyone else who sees this violent stuff in most of the movies and video games of the day? Superfluous content and violent content point to its being written for dramatic effect, like trying to prove something is "real". So who needs to work hard to prove it's all real, the career criminal or someone desperate to disguise what really happened? Histrionics in writing is not presumptive of a career criminal. Sorry, zero for four in hard core criminal presumptions.