The cover-up is a wider conspiracy than the homicide — it includes (for instance) the coroner, etc. I don’t believe they had all those folks on board before the homicide...
I never claimed that they did have all on board before the homicide. But the mere dumping of the body in the remote park with a gun near his hand (the first stage of the cover-up), as well as other events, speaks volumes for the impression that the cover-up - or at least the general outline of it - was pre-planned. You can bet that the specific spot in FMP was not chosen at random or in desperation.