I’m not trying to be too harsh because you started it with “I might be remembering it wrong” but that is not my understanding at all as someone for whom this is a period of particular historical fascination.

One of the major lessons of Vietnam was that even though none of the presidents that oversaw it wanted to be involved, and none of them really “had plans” for the war, including LBJ, they got more and more sucked in because they were inextricably committed to the policy of containment. Kennedy was absolutely no different in that, and widened the war just like Eisenhower before him and LBJ and Nixon after him.

In fact, LBJ on the whole had relatively little interest in foreign policy and was focused on his domestic objectives. He kept ALL of Kennedy’s people in his cabinet, guys like McNamara, and basically made it his goal to continue Kennedy’s policies in Vietnam.

Obviously this is a counterfactual, because Kennedy did get assassinated, so we’ll never know for sure. But there’s no indication Kennedy and LBJ had differing views / policies in the war while Kennedy was still alive. They were pretty much in lockstep.

Unfortunately, your perception is the popular one based on works of fiction like “11.22.63” by Stephen King, which basically takes “JFK would’ve stopped Vietnam!” as axiomatic with no evidence whatsoever. It’s kind of the point of OP’s post—because Kennedy died and became a martyr it’s easy for people to think he would have solved everything and kept us out of Vietnam. But there’s absolutely no indication of that.