I don't remember specifics, but I've heard pretty convincing cases that the Cuban expats and New Orleans mob was involved. Like you said though, they could have been a cog in the wheel. Also, in Matt's Gladio history episode, he talks about how the CIA used organized crime in Europe to launder money through and get jobs done. So it would make sense that they had deep ties with the mob here too.

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I remember hearing somewhere that after an attempt on his life by far right elements of the French version of the CIA, de Gaulle sent a wire to JFK warning him that the same could happen to him. JFK responded something like, "lol for that to happen here, you'd have to have a young president who had some kind of a Bay of Pigs situation oh no haha." I have no memory of where I heard that and I'm posting at work so I don't have time to go hunting all over, but when I heard that, it definitely confirmed my suspicion that the CIA had something to do with it.