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.
You accept that people connected with the mafia would "cheerfully agree to put their lives at extreme risk by assassinating the President". You accept that people "cheerfully agree" to kill other people all the time, even with the penalty of death hanging over their heads. But you somehow can't get your head around these men doing such a thing?
It's like you're deliberately refusing to comprehend that they might do such a thing.
You accept others but not these.
Your point that the men "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." seems meaningless. I can't fathom what you're trying to get at or what the weird factoid regarding Dougherty is about. I'm assuming it's humour but it's hard to say. Maybe you're trying to ridicule something rather than argue it through. I can't tell.
You don't seem to be able to grasp the concept of a conspiracy. By it's very nature it is a hidden thing in which the participants are bound together by the act itself. It's not about trust or faith.
You also don't seem to be getting the concept of compartmentalisation.
LBJ and Byrd are separated from Shelley and Dougherty by Cason. Only Cason knows both groups. Neither group knows the other or has any contact with the other.
Please remember, this is just an idea.
Just a theory.
We can have a discussion about the plausibility of it but now you are expecting me to prove the political ideologies of each man and know their innermost thoughts. No-one has a clue why Oswald might have wanted to kill JFK. He has no motive whatsoever. In fact, JFK's stance on Civil Rights would have appealed to Oswald very much and he would have known that by killing JFK it would be a return to the old ways. Oswald would have been far more inclined to kill Connally or LBJ than JFK. The idea he killed JFK for notoriety then denied all knowledge of it is ludicrous.
Yet many people accept it without any of the kind of proof you are expecting from me.
Hatred for JFK in the City of Hate was rife. Ultra right wing ideologies were rife. A large portion of the Dallas Police Department were Klan members. It is not too much of a leap to assume many others held such views.
In my completely made up scenario which I am inventing right now, Cason is ultra right wing and would gladly see JFK shot. Because of his extreme hatred of JFK Byrd knows he is the man to approach. Particularly as he works in the building he owns. Cason is brought in on the plot and knows of someone who works at the TSBD who shares the same views. Cason approaches Shelley because he is ultra right wing and hates JFK. Shelley has no idea that LBJ and Byrd are involved.
It is Shelley who organises the actual assassination. Someone needs to shoot the rifle and Shelley has the perfect guy in mind. Someone who is easily manipulated and will keep his mouth shut.
All that is left is the patsy.
There is a photo of someone who looks exactly the same as Bill Shelley in New Orleans. He is absolutely identical.
Oswald is in the same photo. This can be used to support the idea that Shelley knew Oswald and knew his politics.
The conspirators are all bound by their hatred of JFK and the genuine belief that they are protecting the country and the American way of life by removing JFK.
In this scenario:
How did Oswald get the job in the TSBD? It would have to be something Shelley organised but this doesn't appear to be the case.
How did LBJ ensure the route of the motorcade? Is there evidence he was involved with this?
Is there any evidence Cason benefitted financially from this? Was his hatred for JFK enough on its own (I like that you think the Cason household wanting JFK shot is "thin gruel". It's actually very handy when making up a theory.)
I'm sure there's lots more to consider but the basic idea is that someone fired a rifle out of a window and someone else was framed for it. It's really not complicated. As already stated, the main obstacle is Oswald's involvement and how that was accomplished.
