Why do you want to believe he did? We have Sheila who had previously voiced fears that her children were evil and would commit certain acts on her, She had previously stated that "all people are evil and should die/be killed" We know that her meds were unstable. We know that her prognosis, because of slow onset of psychosis, was poor. We know that during her last 18 weeks her world must have fallen apart AND YET it was chosen to lay this deed on Jeremy, who apart from being a bit more than a Jack the Lad, had done little to suggest that he could possibly commit this crime.
None of the things you have mentioned regarding Sheila make her a murderer or prove Sheila to be a murderer. On the other side it is often stated Jeremy's arrogance, greed and behaviour post events do not make him a murderer. However, in both cases they may provide some clues.
I have re stated tonight if what Mike says he has is true then there is categorical physical proof Jeremy could not have committed the murders which means it must have been Sheila. However, for some unknown reason Mike will not or does not want to physically reveal or share what he says he has alleged he has in his possession.
Currently and consistently, I believe the answer as to whom committed the murdres lies in the timing and the sequence of the telephone calls. Such events all occured before any silencers were found and do not involve any relatives. For me Jeremy's explanations of these events remains inconsistent with both a number of other independent witness statements and the physical telephone technology that was in place at both the telephone exchange and WHF / Goldhanger at the time.
As soon as Jeremy made contact with the police on the morning of 7th August 1985 the murders could only have heavily involved Jeremy or Sheila.
Jeremy got his defence in first when he specifically names Sheila to the police and outside world.