The plan as I read it was to withdraw forces as the South was able - through our training, assistance, aid et cetera - to take on more of the battle. It wasn't simply to withdraw regardless of the situation on the ground. Two things were to happen simultaneously: we withdraw as they step up. So what would JFK do it the South wasn't able to accomplish that? That's what happened. That's what LBJ faced; and what JFK would have to face. That's why we had to take on more of the effort or leave. Nixon tried to reverse that but it was too late.
As to JFK and a settlement: What's the evidence that Hanoi wanted one? Or Moscow either? After 1964 the Soviets fundamentally changed their approach to SE Asia and, after Khrushchev's removal (he was reluctant to get involved because he believed it would help Mao), began providing massive military and economic support to the North.
JFK was able to settle - for a time - the Laotian crisis without sending in troops because Khrushchev agreed to one. The historian and conspiracy believer John Newman argues that JFK would have dealt with Vietnam like he did with Laos. That is, not send in ground troops. But that ignores the key fact that Soviet policy towards Vietnam was completely different after Khrushchev then it was when he was in charge.
As to LBJ: he uncritically listened to his advisers, the "Best and Brightest", who gave him bad advice and didn't like disagreement among his people. As you pointed out, JFK was much more willing to challenge his advisers, especially the Pentagon and liked hearing dissenting views; so while LBJ went along with their advice, JFK was probably going to reject it.
Anyway: again, what JFK wanted to do is not the same thing as what he was able to do. I don't think LBJ wanted to send in troops either. There are records of conversations he had with people where he said he didn't know what to do. We had to get out but how? What about the consequences?
But that ignores the key fact that Soviet policy towards Vietnam was completely different after Khrushchev then it was when he was in charge.I think that the Soviet policy changes had more to do with a response to the U.S. policy changes that took place under LBJ’s reign than anything else.
By August, 1964, the Johnson Administration believed that escalation of the U.S. presence in Vietnam was the only solution. The post-Diem South proved no more stable than it had been before his ouster, and South Vietnamese troops were generally ineffective. In addition to supporting on-going South Vietnamese raids in the countryside and
implementing a U.S. program of bombing the Lao border to disrupt supply lines, the U.S. military began backing South Vietnamese raids of the North Vietnamese coast. The U.S. Navy stationed two destroyers, the Maddox and the Turner Joy, in the Gulf of Tonkin to bolster these actions. They reported an attack by North Vietnamese patrol boats on August 2, and a second attack on August 4. Doubts later emerged as to whether or not the attack against the Turner Joy had taken place.
Immediately after reports of the second attack, Johnson asked the U.S. Congress for permission to defend U.S. forces in Southeast Asia. The Senate passed the Gulf of Tonkin Resolution with only two opposing votes, and the House of Representatives passed it unanimously. Congress supported the resolution with the assumption that the president would return and seek their support before engaging in additional escalations of the war.
The Gulf of Tonkin incident and the subsequent Gulf of Tonkin resolution provided the justification for further U.S. escalation of the conflict in Vietnam. Acting on the belief that Hanoi would eventually weaken when faced with stepped up bombing raids,
Johnson and his advisers ordered the U.S. military to launch Operation Rolling Thunder, a bombing campaign against the North. Operation Rolling Thunder commenced on February 13, 1965 and continued through the spring of 1967.
Johnson also authorized the first of many deployments of regular ground combat troops to Vietnam to fight the Viet Cong in the countryside. https://history.state.gov/milestones/1961-1968/gulf-of-tonkin
