The lab, the police who supposedly collected it and any other police who would be aware of it including any supervisors they talked to and the family. This is not a small undertaking. The usuall frame job requires 1-3 cops. The more people involved the greater the risk of 1 giving the truth away by accident or if something goes wrong ratting out the whole cast. The risk must be taken into account.
The safest frame job would involve the least number of participants possible. There would be no reason at all to involve the family and risk them telling the truth. Why would the lab go along with it or even engineer it? The average police and family would not have the expertise to engineer it the lab would have to.
1) They had to recognize the shot was of such a nature it would definitely leave drawback
2) to clean out the back spatter from the rifle and pretend it never existed
3) to obtain Sheila's blood and devise a device to spray it inside so it would mimick drawback
The experts each had their own expertise so all the experts used by the prosecution had to join forces. Then they would need to recruit the police who dropped off the sample and had collected it and any other police they spoke to. On top of this they would have to have decided to risk the fmaily being outraged at what they did and ratting them out by asking the family to take part though there would be no need at all if they in fact found the suppressor not the family. Nex they had to pray no one slipped up or talked under pressure.
It is not quite as simple as you make it out to be and there are a lot of risks.
They would simply need to convince the jury that it was possible. Expert witnesses here have often come under HUGE criticism for their willingness to support a certain stance without checking their facts. It was probably worse in 1985. I have already mentioned that crime labs (back then) were NOT independent from the police and many of the SOCO's were just cops - today it is a civilian post. One of the officers who thought Jeremy guilty was a SOCO and would have been familiar with backspatter (although I would imagine most police officers were) and there were 3 samples of Sheila's blood taken at autopsy to use in the investigation.
Why wouldn't the family support the police in their endeavour to convict Jeremy Bamber? They thought he was guilty and such an operation by the police would legitimise the frame up in the eyes of the relatives.
Of course it wouldn't be simply and I have never suggested it would be - the risk, of course would be HUGE. But like you say, who would believe that people including the police could be involved in such an organised sting? Once people already think that, you're half-way there!!
Check the case of Stephan Kiszko who was framed for the 'rape' and murder of Lesley Mullseed. The poor man had a condition that prevented him from producing semen. You would think that any expert witnesses would have needed to be familiar with Stephan's medical records before testifying in condemnation of him because the police knew about his condition but chose to sit on it! Stephan actually confessed (later retracted) to the crime because he was promised he could go home to his mother if he did. He served 16 years in prison for a crime he didn't commit and police knew he was innocent but the frame-up removed the case from their books and the pressure to solve the case. After his release, Lesley's uncle was convicted of the crime using DNA analysis - but too late for Stephan who didn't live very long after gaining his freedom.
Perhaps people don't get framed in the US but there are quite a few examples in British history. Recently Barry George was convicted in 2001 for the murder of TV presenter Jill Dando and in 1989 the Hillsborough disaster involved a MASSIVE cover-up by the police that went to the very top of the force and to the heart of government.