I don't see why BitOfFun would be annoyed about the calls. The court document you're quoting doesn't provide a complete breakdown of everything that happened eg no-one disputes that the police checked the line when JB called but the court document doesn't mention it. Obviously they thought the 4.30am check was relevant because they heard the dog barking so mentioned it specifically.
As for contamination, they would have needed to have DNA from June, Nevill and Sheila. I don't think that's realistic.
DNA knowledge and testing wasn't the same in the 1980s as it is now. But both sides seem to agree the pull-through of the gun was clear but at least one victim had a contact wound that would cause blowback. If the silencer hadn't been on, that blowback would have been in the rifle. But the rifle was clear. If the silencer was on, the blowback would be in the silencer and that is where they found the DNA.
But, as I've said before, I think if we stick to the facts all sides agree on - JB call; Sheila not being an experienced shooter; JB admitting climbing in the bathroom window; etc - then they point to JB. All the 'issues' are attempts by JB to create noise and distraction. He's run a very impressive campaign of constant misinformation.