WI: Lee Harvey Oswald succeeds?

This is above and beyond "What if Jack Ruby never shoots Oswald". What if Lee Harvey Oswald managed to avoid initial detection by the police, destroy the evidence that the rifle was his (the photographs of himself with the rifle), hide his fake Selective Service card and never leaves a palm print on the barrel?

In general, he manages to avoid the most blatant forensic and eyewitness evidence of his guilt. Would he still get convicted, or could he avoid it? If he does avoid it, what are the long term consequences?
 
If Tippet isn't killed, I think the police would probably be under the impression that some guy named Alek Hiddell killed the President. Of course, the evidence would lead them straight to Oswald anyway, but it'll probably give him a day at least. By that time Oswald could well be in Mexico, trying to get to Cuba again. If they let him in, and the police come to the same conclusion as per OTL, Castro is in trouble. Though I'm sure Fidel would be smart enough to return Oswald to the states under those circumstances. (He probably wouldn't get in at all. My guess is he gets arrested at the embassy.)

Although without a car, his transport possibilities are rather limited. (Oswald could not drive as far as I remember.)
 
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