The key to finding a solution to the Korean standoff, or to knowing if there even is one, is knowing the interests of the various players. Suffice it to say that both Koreas would like to absorb the other one and emerge with a unified Korea under its regime. But there are many outside powers in northeast Asia that have interests as well. Traditionally the three most powerful countries in East Asia in modern times have been Japan, China, and Russia. China and Russia are fated to live bordering one another, but Korea separates the two from Japan. This is why when Japan became an imperialist power in the early twentieth century Korea was the second country it colonized, after Taiwan. This gave it an invasion route into Manchuria and also prevented Russia or any other country from invading Japan via Korea.
Once Japan lost World War II and renounced aggressive war, it still had an interest in having friendly or weak powers in the peninsula. Thus the American occupation of South Korea was ideal from a Japanese perspective. Japan would probably, however, just as soon see Korea divided and preoccupied rather than allowing it to become the vigorous economic competitor that the South has become. So, from the Japanese perspective a divided Korea would be ideal. The particular peculiar nature of the North Korean regime, however, provides a danger to Japan. It has aggressively and provocatively fired missiles towards Japan, made threats against Japan, and kidnapped Japanese citizens for the purpose of forcing them to become Japanese language teachers in North Korea for spies and defense personnel. If North Korea could refrain from this type of provocative action, it would cease to be a threat. But this type of action seems to be endemic to the regime.
China similarly has an interest in a divided Korea rather than a powerful American ally on its southeastern border that might serve as a magnet for defectors. China's large army and nuclear weapons are sufficient to deter any threat of invasion from a united Korea, but the attraction remains. Much better to have a weak, if somewhat erratic and eccentric North Korea on its border. The wave of defectors from North Korea can be dealt with through individual deportations.
Washington has an interest in preserving a free South Korea, but it can do this at a much lower level of expense than at present. South Korea has a GNP some twenty times that of North Korea and a much larger population. It should be able to pay for its own defense. The rationale in both Seoul and Washington for the presence of American troops in Korea is to serve as a trip line to give the American nuclear guarantee credibility. Both are worried that without this guarantee, North Korea could easily invade and devastate the South Korean capital, Seoul, which is located only about 50 miles from the border. But where South Korea chooses to establish its own capital is its affair--and it should take the consequences of that decision. South Korea has several major cities and it could easily transfer its government offices to one of them--as Israel did in 1948 from Jerusalem to Tel Aviv. So whether Seoul develops its own deterrent to prevent the North from shelling its capital or moves that capital to another city (or both) is up to it. American taxpayers should not be expected to pay for the privilege of defending the South from attack from the much weaker North.
Japan, China, the United States, and Russia would all be well served by an agreement by which Pyongyang agreed to give up its nuclear weapons in exchange for guarantees that the South would not invade or foment regime change. Washington should be willing to offer such guarantees to North Korea. Japan became a problem for Washington when it began to threaten its neighbors through expansion. The fact that the emperor was regarded to be a god was not considered a threat. The same should hold true of Kim Jong Un in the North. While he is an affront to human rights, the savings from American expenditures in Korea could be reinvested in bulking up the American naval deterrent to aggressive Chinese actions throughout East Asia.