There are two PODs to choose from: July 8, 1960 and November 22, 1963. By "defuse" I mean "Korea", not "Versailles". Bonus if RFK becomes VP in 1964 and Double Bonus if LBJ dies before January 1967, which gives RFK the opportunity to be a two-termer.
I know this is tough, but it is not ASB. It is impossible after January 25, 1967. I'll explain why later.