Correction Scipio, The initial wound on Sheila's neck did not sever a 'major artery' in Sheila's neck it was 'soft tissue haemorrhage' to the 'right external jugular vein' soft tissue bleeding from a vein is VERY different from the severance of an artery. The severance of an artery causes severe bleeding often shooting from the wound due to the pumping of the heart which propels blood through the artery. Blood in the veins is blood returning to the heart to be oxygenated and it flows it isn't pumped. This is why the amount of blood which appears to have collected under Sheila's right armpit is puzzling to me. I cannot understand how that blood settled there unless her head neck was resting near to it. Imo.? I know there are blood trails but it is still an awful lot of blood. 
Also because it was a wound to a vein, not an artery this is the reason Sheila could possibly have been conscious after the first wound, it is quite possible she could have stood up and wandered about or she could have shot herself again, it is not an impossibility.
I stand corrected a major vein severed not artery. That doesn't change the fact that the blood staining indicated she had not been standing upright walking around, had she been upright the blood would have gone down her gown. Nor would it have gone down her shoulder if she was lying flat. Clearly she was seated against something at an angle sufficient to allow the blood to flow down her shoulder and side breast area. That is also why she was able to have the blood drip down her arm towards her elbow.
The jugular vein handles the blood in the head. Her head was higher than the rest of her body and the blood in her head leaked out through gravity even after her heart stopped beating. This just confirms she was not lying flat when she was shot, she was seated propped against something.
Nor was she lying down flat when she was shot because if she had been then the blood would simply have gone down the side of her neck to the floor. She was seated against something at an angle which caused her head to be above her shoulder and this caused the blood to flow down her shoulder/the side of her breast.
Jeremy eventually decided to move her flat so that he could lay the gun across her body- he felt that would be the best way pf presenting as a suicide. In so doing he broke a cardinal rule, you should not move bodies because it can be detected. He figured they would believe Sheila moved herself. Vanezis didn't put enough thought into it to use such as a basis to challenge the suicide police theory. He seemed to annoyed by the amount of work 5 autopsies in a row is a lot and just went with the flow.
On appeal prosecution experts recognized she was seated when shot and subsequently moved flat by someone else. They rejected Vanezis' simplistic explanation that after the first shot she managed to stay seated though not propped against something, got so much blood on her shoulder/breast area in 5-10 seconds and then she instantly fell flat on her own after the second shot. They said she would have fallen back after the first shot unless propped against something. Quite clearly Vanezis was inept in not recognizing what the experts recognized on appeal. Vanezis should have stated such to police from the outset. That could have changed the theory police were operating under. If he told police such certainly they should have changed their theory and started to investigate it differently- whether they would have who knows. But it would have provided even more fodder when they looked at things and decided to replace Taff Jones as top dog.
The Court of Appeals quite correctly held that the assessment was not new evidence. They had this evidence from the outset and their failure to properly analyze it until after the conviction is too bad they could not raise it on appeal.