This seems to me the simplest scenario - regardless of the perpetrator.
Jem leaves his cottage and cycles to WHF. He uses the saw blade to gain entry through the shower room window. He takes the kitchen phone off the hook - disabling any attempt by parents to make an outgoing call from the bedroom if they heard him downstairs. He gets the loaded rifle from where he has hidden it in a cupboard earlier - not leaving it out as he had claimed in case Nevill put it away somewhere where it might take a while to find - attaches a silencer. He has to use a silencer to minimise the chance of shots being heard by anyone nearby.
He climbs the stairs - his mother and father have not heard him - he enters their room puts 4 into June then 4 into Nevill. He goes to the boys' room - it takes him a while to summon the courage to shoot them - but he does so with one bullet each.
He believes all but Sheila have been incapacitated so he goes downstairs to reload in the kitchen. Nevill has managed a partial recovery comes downstairs, staggers in and a fight ensues - silencer gets chipped paint on it - Jem prevails against his weakened father battering him with the rifle butt. Nevill slumps where he is later found - Jem puts 4 more into Nevill's head killing him.
Jem fully reloads and goes back upstairs to find Sheila in the bedroom with June who has made progress crawling to the telephone. He puts more into June then at gunpoint commands a terrified Sheila to lie down and close her eyes. He shoots Sheila in the neck but she wriggles at the touch of the silencer so he misses the clean shot - realises he's made a mess of it but needs to wait to see if the shot is fatal. He goes into the boys bedroom puts all bar one bullet into them to make it look like a maniac attack.
Back in parents room Sheila is not dead - he can't risk her surviving but can't wait too long for her to die naturally. He waits but she still won't expire. Finally unable to wait any longer he puts the fatal shot into her head and leaves the empty rifle with her. He takes the bedroom phone downstairs and after removing the existing phone (putting it under magazines) plugs it in - dials his cottage and leaves the phone off the hook - creating the scene for the later "Nevill phone call". He puts the silencer in the cupboard where it is later found - he's not worried about DNA as the technology is in it's infancy and he doesn't know about it.
He exits the house using the window above the sink - banging it shut so the latch falls and locks it from inside. He cycles home.
That matches the crime scene evidence. Except June was shot 5 times in bed.
Julie said the twins were shot first. If correct I believe it was once each.
Don't believe Nevill fell where he was found. Head in a coal scuttle.
Also believe it likely he disabled the phones upon entrance. No reason why the bedroom phone should be im the kitchen.
The kitchen attack was so crazed, believe it would have been after he had chased Nevill. An injured Nevill upstairs would want to save energy & try to stop Bamber when he gets back upstairs.
