The absence of blood in the flat is a problematic. VT tells a story to explain everything ... there's something about the back pathway that he had to explain. He said he bought rock salt, presumably because the back path was slippery and he said he found it slippery when he carried Joanna to his flat. He said that he had to put her down because she was heavy. Was he countering evidence found on the back pathway ... evidence like perhaps he attacked her there, she ran back to her flat and he ran after her ... that's when the coat rack was knocked over? Was she running into her bedroom and that's where she was killed? Why did he take her to his flat? Did he really do that and if so why? It would be safer for him to take his bike cover to her flat, wrap her up and put her in the car. He's a people flow person ... it makes no sense that he first took her to his apartment to wrap her in a bike cover and later took her to the car. Did he attack her close to 9, per screams and timeline, but he kept her in his flat and toyed with the body for 30 minutes before he contacted his girlfriend, and then he went to the grocery store? Why is he connecting 9:30 to the murder ... unless he is trying to avoid that 30 minute time period between the murder and the shopping trip.
I think most people would accept that he was in a panic and frantic for those 30 minutes ... but from VT we have an attempt to change the time of death to 30 minutes later. Why does he feel the need to explain or eliminate that 30 minute interval if everything was on the up and up? After an accidental murder, 30 minutes are easily understood as complete panic ... but not for VT ... he simply went back to his flat, texted his girlfriend, put his neighbour in his car and bought beer and crisps ("crisis", per VT ... quite the Freudian slip). Still, there are 30 minutes missing in VT's accounting.
If you believe the case for the prosecution, JY was killed very shortly after she got home. That doesn't look great for VT. It suggests that he was waiting for her to get home and planned to have some sort of contact with her. (It's not really relevant to whether he murdered her though. To prove murder, the prosecution need to convince the jury that he knew, when he had his hand round her neck that it would seriously hurt or kill her).
Also, if you believe the prosecution timeline, the text sent to TM at 9:25pm was after JY was dead. It was a calculated attempt to show that he was quietly sitting at home, bored without TM there.
If the jury find him not guilty of murder, and I'm guessing here, it may be that a lot of what the prosecution are suggesting could be aimed at influencing the judge when he deals out the sentence for manslaughter. (e.g pre-planned, calculating, cover story etc etc)
If however you believe the timeline the defence suggests, VT sent the text to TM at 9:25pm and set out for Asda. On passing JY's window, she waved him into her flat. He misread her allegedly flirtacious comment as a come on, went to kiss her, which according to VT was in no way a sexual activity. She screamed and in trying to calm her down she went limp and died not having put up any kind of struggle.
In his version of events, when he went to Asda and texted TM at ~10:30pm he was in a blind panic. He just picked up on his original planned shopping trip and "reached out" to TM
As for taking her body to his flat, he couldn't know that JY wasn't expecting guests. Someone could turn up at any moment and find her body. He had to move it quickly. His car was on the road. He couldn't carry her straight to the car. He had to move the car round the back near to his flat and wasn't going to risk leaving her in her flat whilst he did that.
Did he put her down when carrying her to his flat or did he drop her? If he dropped her perhaps that might account for the blood. It would also explain the need for the rock salt and the fact that there hasn't been any mention of blood in the flat. It might also explain why he put her inside the cycle bag so as not to get blood in the car.
ETA: We don't know for sure there was no blood in the flat. It may be a fact that is not contested by the defence so there's possibly no need to prove it in court