It's possible for both things to be true, that Oswald did it and the CIA still had to perform a massive cover-up (for institutional self-preservation, as you pointed out). If you view Oswald as a "Wannabee" who tried to ingratiate himself into the intelligence community and failed (because he was a loser and also mentally unbalanced), you can apply Occam's Razor and come up with a plausible way to explain the CIA's odd behavior as pure bureaucratic CYA. And when you add in how scared both the US and Soviet intelligence communities were after the Cuban Missile Crisis, the picture that comes into focus is just a banal story of a loser who got ridiculously lucky in carrying out his true motivation, to throw a big fat middle finger at the CIA.
I think it’s as likely as him being killed right before he reigned in the Federal Reserve with Executive Order 11110. That is, not very likely. It sounds attractive on paper but neither theory has anything more that extremely tenuous circumstantial evidence to support the claim.
They had the ability to do it and probably get away with it, and they had motive: self preservation.