The only people we know for certain with opportunity to both kill JFK and mutilate his corpse were members of his Secret Service detail. If the conspiracy goes beyond that group, there's no way to tell for certain, but its a good starting point. And to be honest, its usually the praetorian guard responsible for assassinations anyway.

The more important issue is I'm not convinced Kennedy's death was a bad thing, for the country or the world. He played brinkmanship with the Russians and nearly ended all life on Earth. No single person should get to decide the fate of all other life on Earth. Luckily we were able to pull back from the brink, but his willingness to drag us so close to annihilation was beyond the pale. Killing him, though tragic, might have saved the species from extinction. Johnson, though a psychopath and war criminal, at least worked with systems to protect humanity from extinction.