DEFINE THE MISSION. Make sure everyone knows what the goal is and what success looks like.
Go big, straight out of the gate.
Find, fi xand defeat Giap's conventional forces (including killing him if at all possible, man was bloody genius at asymmetrical warfare) Take control of the China/Vietnam border and fotify the hell out of it Declare and enforce a hard blockade of the waters surrounding Vietnam. Drive all surviving NVA forces out of the cities and into the countryside. Simply take command over all of the country. Only use thoroughly vetted Vietnamese leaders, hammer flat any and all corruption.
If firepower isn't solving the problem, the problem is that you are not using enough. Spend big money on "hearts and minds" especially offer huge rewards for information that leads to the elimination of Viet Minh and VC cells.
In short do what Alfred says he and a some of his friends did in one of the Batman movies. Enemy is hiding in the forest? Burn down the forest.
Once you have achieved the defined mission goals hand over the keys to the, hopefully well chosen leadership of the democratic Vietnam. Tell them Good Luck, and y'all on on your own.
Tell the Soviets and Chinese, and make sure that you are serious as Death itself, that the Blockade is permanent and any attempts to supply revolutionaries in Vietnam will be seen as a direct invitation to do the same in the Warsaw Pact and Tibet.
Go home. Mission accomplished in every detail.
Sit and watch as within ten years all that hard work goes down the tubes due to internal corruption and regionalism in Vietnam,
I've recently finished reading Max Hastings book 'Vietnam: an Epic Tragedy' and i'd like to weigh in here. Because it sounds to me this scenario of "gung ho" is like a typical Westmoreland and even Abrams type of response to the question they themselves were asked by US presidents. And its wrong. How many US soldiers casualties are we talking about here if thats the game plan? "Go big" is what both generals did, they used airpower and search and destroy(later, clear-and-hold, essentially the same), in WW2 mindsets. Think of operation rolling thunder, what did that do? Nothing, unless the US has so many boots on the ground it would make operation overlord look like a training op. and what would be the casus belli?
Vietnam didn't work like that, it wasn't occupied France or fascist Japan. The US was fighting communism, essentially fighting China and the USSR, on vietnamese territory, a proxy war. But the vietnamese were fighting an independence war, a nationalist war. They'd do anything. They did anything and everything. Its brutal, criminal even, but they did what won them the war, the US and south vietnam, did not. And it was not having superior forces, firepower or control. It was spirit.
The biggest issues i think the US had was thinking they were fighting 'just' an army and 'just' a guerrilla movement. But they were not, they were fighting all of vietnam. Because even the south vietnamese were part of the movement moving towards independence, a way to be rid of the overbearing foreigners in their country, wether it be French, Japanese, Chinese or Americans. They hated communism, more and more as the war progressed, but in the back of their head they still dreamed of independence, South Vietnamese are not a different people from the North, only in location. And at first they believed that the American were going to be able to give it to them, with a lot of costs they were willing to accept, to be independent and not under the opperssion of Stalinism. But eventually, as is with all violence, there is limit. That limit was already reached in OTL, imagine what will happen in your scenario.
You might think that the North isn't prepared for something as big as your plan in 1959, that it will collapse because, firepower. Well, tell the French that. And what did the US learn from the French experiences fighting? Nothing.
Thinking bigger in such a situation would only cause more casualties, on both sides but mostly amongst the civilian population, because that is what you are fighting, it is a civil war. Fighting like that would simply empty the country, deplete it of a fighting, governing and producing population leaving only old people and children behind. and about ten times more US casualties.
And not only Vietnam if you gonna do what you are suggesting. you'd have to do the same to Laos and Cambodia.
What is then the ultimate goal? You'd have a free, independent Vietnam? Or are Americans just the new French? or Japanese? Or Chinese? Just the same oppressors in a new uniform. Vietnam won't accept that, it won't be over.