Of course you did 
Of course the police had something to gain! A successful conviction and of course it wasn't guaranteed which is why a silencer was produced and a coached star witness. Were the officers involved in the Birmingham Six case convicted? Were the officers involved in the Stephan Kizsco case convicted?
OBVIOUSLY it's never been proved because if it had, he would be a free man!! However, just because it hasn't been proven, doesn't mean they didn't!
The police on their own would have lacked the knowledge and skill to pull it off.
First they would have needed to know that fatal wound would have caused blood to enter the suppressor. Only the experts knew that it would.
Fletcher and Hayward would have to have been the masterminds of it.
Hayward the one who checked the rifle for blood and found none. He would have found blood had the suppressor not been used so he would have to have lied about not finding any.
Fletcher would be the only one to know how to spray blood inside to make it resemble spatter. Why would he bother though if he was the one doing the tests he could just lie about it. But he didn't lie the defense expert found microscopic drops of blood on the first 8 baffles.
There is no evidence that any of Sheila's blood was missing from the samples so they would have to have found another source of group A blood.
They would have to have involved enough police to get them to speak to the family and get the family to lie about there being blood in the suppressor when they turned it over and maybe even the police and family lying about how it was turned over.
Then they get Julie involved in the lying.
The more people involved in a conspiracy the more people who talk and faster it gets caught. They would especially not want to let non-police know about it because they could mess up or rat the out and end their careers.
The grand conspiracy is highly unlikely.