WI US Invasion of Cuba, 1963?

I've posted various questions relating to this subject before, but here i'm looking more for the military aspects of the question.

For a TL i'm currently working on, I have the JFK assassination going differently. Rather than Lee Harvey Oswald being determined (officially) to be a lone wolf, he's instead part of a domestic Communist terror group, with links to/support from the Cuban government. Obviously, LBJ and the rest of American leadership doesn't take this well. Assuming that the Soviet Union throws Castro under the bus, and isn't willing to go to war with the US over Cuba, what would a US invasion of the island look like? What would the logistics be like, and how long would it take to have effective control of the area? I imagine that the conventional war wouldn't take long, with an incredibly p*ssed United States jumping at the opportunity to finally take out Castro, but what about guerrilla fighters? And who would wind up leading the next Cuban government?
 
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