The failed decapitation...
You make an assumption here that I do not believe can safely be made - i.e. that it was an attempted decapitation.
You speak only of the cut-throat and eyelid injuries, concluding that both were inflicted with the same weapon. What about the others?
The pathologist dempnstrated that the murderer would have to have held the knife at the end of the handle(were it a 4 inch blade) with the tips of his fingers - do you accept this as the probable method used to inflict this injury?
I don't believe it was ever ascertained what knife was used to carve the initials in the tree. They were carved before the murder at a spot Jodi and Luke were known to hang out, so I don't see the relevance of the distance from the murder scene.
The skunting knife bought after the murder was handed to the police, and bore no forensic evidence of the murder. The other lock knife claimed to have belonged to Luke was handed to police by Ferris, who in turn claimed to have stolen it from Luke, even though other witnesses insisted it was always Ferris's knife. Other knives retrieved from Luke were a swiss army toolkit (broken) and a pen knife. An old decorative sword (completely blunt and rusty) was taken from his bedroom wall, along with an array of kitchen knives, stanley knives from the garage etc, from the Mitchell household. The evidence of Luke's "fondness" for knives is of the same calibre as his "obsession" with Manson.