This is what I believe. I believe Jodi left to meet Luke and met him around 5.05pm. I believe he walked her to her death scene. I believe he murdered Jodi. I believe he was wearing his parka at that time. I don't believe he was at home when his mum and brother initially said he was. I believe he murdered poor Jodi and then I believe he had help. I believe that help came from his brother and mother. I believe that someone swapped jackets with Luke. I believe someone gave him the green bomber jacket and took the parka. I believe this was arranged by phone, hence the deletion of almost everything. I believe that's why RW and Fleming witnessed LM in a parka and why the positive identification by the school boys identified Mitchell in a bomber jacket. I believe someone swapped him jackets in the interim. I also believe this is why SM, wants a quiet life. Where was LM from the back of six till half seven? He had far more time than you can account for. I believe LM murdered his girlfriend and I believe he mutilated her body post mortem. I believe he did it alone. IMO
But AB made it abundantly clear in court that the jacket Luke was wearing was not a parka but of the jackets she was shown a photograph of, the parka was the nearest. So how did Luke get the parka in order to kill Jodi in it and when? Did Shane bring it to him? Why did Luke say he needed it?
So Luke when seen by AB was not wearing a parka but a green fishing style jacket with a pocket on the sleeve. Somehow after being seen by AB he obtains a parka in which to kill Jodi and then, again somehow, convinces his brother, who until that moment knew nothing about the murder, to bring him another jacket and take the now, I assume, blood soaked parka home. Does that really sound feasible to you?