Jim,
I have a feeling, after reading much (but not all) of the JFK Assassination posts on this site, that many people (perhaps not yourself) don't realize the Warren Report was a conclusion based on 26 volumes of testimony taken during the investigation in 1964. Oswald's connections to the CIA, Hosty's name in his notebook, the Moorman photo, the Umbrella Man, the tramps, Sylvia Odio, and all the other "smoking guns" are discussed at length in those 26 volumes. They were and are not secrets.
The Report is a "best guess" but has, after forty years, proved to be a solid one, surviving congressional investigations, committees, and countless scientific, accoustical and ballistic reenactments. The Freedom of Information Act has even made the lone assassin conclusion stronger. Harold Weisberg, Mark Lane, Richard Popkin (his "The Second Oswald" was written in 1964, I think;so much for the "new" theory being bandied about) all made names for themselves as whistle blowers of the "dark side" by using the information freely available in those volumes. A government with something to hide doesn't let people check its books, or, for that matter, let them publish expose's that bring the plot to light.
I understand now what you meant by the coin toss. But I disagree with your point that we can choose how we feel about Oswald. That would not be intellectually honest when you face, pardon me, but this metaphor is appropriate if insensitive, the tsunami of facts that overwhelmingly convicts him and him alone.
There is an old saying, A lie has speed, but truth has staying power. The lone assassin conclusion has held up a mighty long time.