Call me old fashioned, by I still go with Jim Garrison's theory that Oswald or someone impersonating him had approached the Soviet and Cuban embassies with the full knowledge that his presence would be noticed by CIA surveillance in order to implicate communist powers. My number one suspects were the nest of Anti-Castro fanatics in New Orleans and Dallas - both Americans and Cuban exiles - who had been sponsored by the US intelligence community, organized crime (which was the CIA's secret partner in assassination plots in those days), and right wing business interests, in their secret war against the communist Cuban government. Oswald was known to have had associations with these professional Anticommunists who had been employed as contract agents by the CIA in New Orleans, in particular:
CIA and Mafia pilot David Ferrie, who Oswald had had a preexisting relationship with.
Ex FBI higher-up and Office of Naval Intelligence operative, and die hard segregationist, Guy Bannister, who had run an Anti-Castro training camp and gun running operation under cover of a private detective agency, and whose specialty had been infiltrating leftist organizations with undercover agents.
Not to mention the host of Cuban exiles in the New Orleans Anti-Castro underground, many with intelligence and organized crime associations.
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-Bill, otherwise known as Kraichgauer