An interesting post Adam which considers several pertinent issues.
Firstly, the claim that a third party did it is invalid and preposterous for so many reasons all of which you have rightly stated have been gone into in some depth here previously. For the benefit of anyone who is not familiar with the case I will briefly explain. The farmhouse was still secure when police arrived on the scene, all external doors were locked and barred from the inside. The windows also appeared to be secure and properly locked, in fact the police checked on this after gaining access to the property and as far as they were concerned nobody entered or left the house after the family had retired for the night. This entire situation was designed to give the impression that it was an inside job, that Jeremy's adoptive sister Sheila had carried out the killings before turning the gun on herself twice. Jeremy never revealed anything which could dispute that understanding but it was all to change.
What the police didn't know and might never have done had it not been for an error of judgement on Jeremy's behalf was that he could get into the farmhouse at will, day our night and undetected. This was revealed when a matter of weeks after the murders Jeremy needed to get into the farmhouse to get his passport and other possessions for a trip to France. He didn't want to alert the housekeeper who retained keys to the property in case she contacted the police so he sneaked in using a window which he knew could be opened from the outside. He had thus unintentionally revealed how he got in on the night of the murders. The inside job theory thus began to fall apart and Jeremy was arrested en route from Dover as he and friend Brett Collins returned from France.
Now we turn to Sheila Caffell whom Jeremy Bamber claimed from the outset had committed the murders. Thanks to the trail of evidence, the sequence of the shootings for the most part can be deduced. We know that Nevill and June Bamber were shot in their bedroom, June as she lay in bed and Nevill as he approached the door. We know that Nevill, although badly wounded, was able to make it down the stairs in an attempt to summon help. We know that he fought with his assailant in the kitchen before being overpowered and bludgeoned by his attacker using the rifle. We know that he was shot in the head again where he sat before collapsing forward ending up seated but drooped with his face in a coal scuttle. The question then arose as to how Sheila could have managed to do all this without sustaining a mark on her, without chipping a single nail and without a drop of anyone else's blood getting on her or her nightdress. The simple answer is she could not have done so.
Jeremy Bamber's masterplan to wipe out his family went wrong the moment he fired the first shot. He badly misjudged the capability of the .22 calibre low velocity rifle bullet. Fine for shooting pigeons and rabbits but not human beings. He found out very early that one or two bullets would not kill, he had to use more bullets than he had counted on, he had to seek out more ammunition. He was forced to fight a wounded Neville in the kitchen, something his sister could never have done. When it came to shooting Sheila in an attempt to misrepresent murder as a suicide, it again went wrong. The first shot only stunned her forcing Bamber to shoot her again where she lay, a double shot suicide being possible but very unlikely.
Clearly what was intended to look like four murders and a suicide went wrong from the start. Only one person knew how to get into the farmhouse undetected whilst at the same time not attracting an alert from the farm dog outside. That same person was also very capable of handling a rifle and possessed the strength to wield it in a fight with a man who was both very strong and over six feet tall. That man for all the aforementioned reasons was Jeremy Banner.
Jeremy Banner knows very well that his sister Sheila Caffell did not harm anyone, his denials however are both false and so predictable.