Adam your version of Jeremy is quite an enigma
Clever enough to plan two shots
But stupid enough to tell his girlfriend
Clever enough to plan a call from his father
but stupid enough not to wait a while and make it a proper emergency call rather than dilly dally
Clever enough to LOCK a window behind him
but stupid enough to tell the police he could get in and out of the house
He was such a namby pamby he could not shoot rabbits
but could shoot his whole family and stand calmly next to police
He was not speaking to his mother ( according to you )
But he was happy to go round for supper.
Clever enough to totally dispose of any forensic evidence
But dumb enough to leave the silencer with a Blob of blood .
You are weaving an intricate personality .
And before you say anything there is a source that he was thoroughly tested face to face ( not by someone who had never met him , and he was not a psychopath.
All that is correct. And plausible.
He may have spent a couple of hours reading up on whether two shot suicides happen. To cover himself. He spent months beforehand telling Julie of his raw deal. So no point in not admitting his involvement afterwards.
Calling Neville as part of the murder suicide frame was his best option. The execution was not great.
The police asked him about the windows. He would know that Julie and the relatives had told the police. And that the police would check themselves. So he told the police, but not that he could lock them from outside
He went to shoot rabbits. But didn't. And left a loaded gun for Sheila.
He testified himself that he had a poor relationship with June. But still went round for supper. On the massacre night anyway.
There is a lot of forensic evidence. Including the silencer.