That would be a very interesting novel.
Yep, something along the lines of JFK does get shot, but not fatally. LHO is captured alive and gives up the Mafia/Military plotters, resulting in the end of organized crime. JFK, fully recovered, is re-elected, takes out Castro. Cuba and Puerto Rico become states. He continues his tax cuts, the economy goes wild and Viet Nam never happens as the Commies are too afraid of the USA.
Hmmmm....