I will try once more and then I won't beat it to death. You may have the last word. I'm truly puzzled as to why you view your scenario as completely plausible and I'm having difficulty seeing it.
Yes, your theory has minimal participants, so that’s a plus. But those five participants extend from the Vice President of the United States to a possibly mentally challenged guy who is still a lowly shipping clerk after eleven years of employment at the TSBD. (Dougherty lived until 1994, even though in your scenario he would seem to have been a prime candidate for an almost immediate "mystery death."

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As I understand it, each participant has to have complete trust in the participant immediately below him. LBJ has to have complete trust that Byrd will somehow get the job done without knowing the details. Byrd has to trust Cason and deals only with him, Cason has to trust Shelley and deals only with him, and Shelley has to trust Dougherty. In other words, LBJ and Byrd do not sit down and hatch a plot involving Cason, Shelley and Dougherty – is this not correct? This is what I mean by each having “100% faith” in the participant below him.
Or is the theory that Byrd did outline his entire plot for LBJ and that Cason and Shelley and perhaps even Dougherty were fully informed, at least about everything except LBJ's involvement? I thought the idea was to keep each stage as fully compartmentalized as possible for purposes of deniability – Dougherty knows nothing but Shelley, Shelley knows nothing but Cason, Cason knows nothing but Byrd.
Either way, LBJ is either knowingly putting his fate in the hands of characters like Cason, Shelley and Dougherty or in “whomever Byrd finds to carry out the task.” Even in LBJ’s precarious circumstances, this seems to me like a fantastic risk for LBJ to take. As I said, I can see LBJ using his many connections to find a single gunman answerable only to him and under his complete control more easily than I can picture him involved in a plot such as this. I don't see how this qualifies as "bananas."
Next what I’m talking about is any evidence that Cason, Shelley and Dougherty actually were near-insane right-wing fanatics who would have been readily amenable to an assassination plot on strictly ideological grounds. The “shoot JFK” statement attributed to Cason at a party two years before the JFKA seems like pretty thin gruel.
My main issue is that you write as though this would have been practically business as usual, as though they were planning the robbery of a Circle K in Plano: Byrd suggests to LBJ let’s whack JFK, LBJ says go for it, Byrd tells Cason to whack JFK, Cason tells Shelley, Shelley tells Dougherty, and Dougherty says OK I’ll do it. In my mind, there is something missing as to why Cason, Shelley and Dougherty would just cheerfully agree to put their lives at extreme risk by assassinating the President. You make the connection with their supposed fanatical hatred of JFK, but where is any evidence of this? And then they all just return to their mundane TSBD existences the next day? It just doesn’t strike me as being as plausible as it obviously does you. For the Mafia, on the other hand, this really would have been business as usual.
(The new avatar is my actual maternal grandfather, Theo Skladany, who is the only member of the family who was not green and did not have webbed fingers or insectoid eyes. We don't know where the heck he came from.)