My best bet, and this admittedly has holes all over the place, is:
After Japan takes over Korea, research finds that the Japanese and Koreans and actually descended from the same stock (which is true in RL), and begins the process of making Korea and Taiwan be an integral part of Japan.
The Empire of Japan slowly begins to integrate Koreans and Taiwanese as Japanese, resulting in a rising standard of living of Koreans and Japanese. Crimes are still committed, of course, but the Japanese superiority complex towards all other Asians starts to die off.
The Navy and Army fight in 1935, but Japan still declares war to take over Manchukuo, which they largely succeed in doing by 1938. Japan joins the allies in 1937, and the Japanese militarists propose to settle Manchukuo and parts of Korea and Southeast Asia with European Jews. Hitler, who just wants them gone, accepts this. This results in over one million European Jews shipped across Russia between 1938 and June 1941.
Pearl Harbor still happens, and the USA still declares war. Results are largely the same, though the considerably bigger Japanese Navy puts up a much more stubborn fight. The finisher battle is in January 1946 off the Phillippines again, at which time as American forces are joined by British, French, Canadian, Brazilian and Australian forces. This however results in a much bigger mess for both sides - USS Saratoga and two American BBs, along with the French Jean Bart and British Ark Royal die off the Phillippines, but the Allies still win. The Soviets are too devastated by the European War to bother attacking Japan, so Japan keeps Sakhalin Island. The atom bomb is dropped on Hamamatsu on April 18, 1946, followed the second on Hiroshima on April 22. Japan surrenders April 30, 1946. (Bomb research takes longer as the US focuses resources on bigger forces.)
Japan takes its defeat hard, but as Japan, Korea and Taiwan are a unified nation in all but name, and the Americans, seeing Chiang losing in China and wanting a capitalist superpower to hold back Mao and Stalin, demand Japan disarm but allow them to keep defensive military capabilities and allow Japan, Korea, Taiwan and several islands in the Pacific to stay Japanese. The new nation is the United Republic of Japan, Korea and Taiwan - usually just referred to as Japan, though many Koreans and Taiwanese like to point out about their lands.
Japan, noting how hard the Jewish immigrants fought - a bunch rose through the Japanese military ranks very quickly, due to their fighting - and also noting that many around the world have much the same work ethic and ideas as them, reforms much of their ideals - including the tossing of just about any racial dogmas.
Focused on its own rebuilding in the 1950s and 1960s, Japan has little room for social. The Americans keep the PRC from doing anything in Korea. Kim Il Sung is executed in 1955 by the Koreans for treason for trying raise a civil insurrection. Major manufacturers and companies grow in all three major areas, and by the 1970s Japan is well into the first world. Tokyo hosts the 1964 Olympics, which was largely seen as Japan's powering back onto the world stage. (Seoul hosts in 1980, Taipei in 1996.)
In the 1970s, Japan starts taking in more immigrants. The first arrivals are usually Filipinos, Chinese, Indonesians and Latin Americans, and some Australian aborigines. A steady flow of Jews also continues coming in the 1970s. By now, many Japanese, Korean and Taiwanese companies - Sony, Sanyo, Lucky-Goldstar, Toyota, Mitsubishi, Acer Electronica, Toshiba, Hyundai, BenQ, Nissan, Honda Motor, Evergreen Marine, Nautica - are world leaders, and gaining growing market share abroad. Their phenominal profitability in the 1980s fueled powerful economic growth in the 1980s, and the following draw for many.
In the 1980s, Japan's prosperity resulted in a change in the eyes of many Japanese of what life meant. The country's once small population growth rate rose to replacement level in 1993, and the unified Japan by the late 1980s was stagnant in industrial growth, but had instead shifted its growth to arts, design, research and development, recreational activities and other activies beyond just producing.
This resulted in more growth in immigration during the 1980s. the Nikkeijin of South America almost entirely came during this time, in many cases bringing Argentine, Brazilian and Uruguayan friends with them. China's bad relations (which persist even today) with Japan mean that most Chinese go to Taiwan first, and then spread out across the nation. Others start arriving in the 1980s, including Indians, some Africans, and whites - usually Americans, Australians and South Africa's Afrikaners. After the fall, this number is added to by Russians fleeing the crumbling, scar-ridden Soviet Union.
By 2000, Japan has a population of 241 million, of which 21% is either partially or completely not of Japanese, Korean or Taiwanese stock. In the largest cities, especially Tokyo, Seoul, Osaka, Pyongyang, Taipei, Nagoya and Sendai, that number grows to roughly 30-40%. Japan's first immigrant-descended Prime Minister, David Aonkasi, takes office in 2002 and serves four years. Immigrants and their descendants are still said to treat women better than their Japanese counterparts, a somewhat-stereotypical problem that often irritates the hell out of Japanese men.
Tokyo is the center of an empire, a high-fashion design center which counts as one of the world's centers of finance. Many companies have their headquarters here, though many more have long since moved to other parts of the nation. Urban renewal in the 1980s and 1990s resulted in thousands of acres of greenbelts being carved through the dense city, which are kept spotless. The country is hooked together by several high-speed rail routes, and a large fleet of high-speed vessels that carry cars, trucks and people from island to island and to the Korean mainland at speeds often topping 55 knots. Over a dozen airlines serve the country, with Japan Air Lines, All Nippon Airways, Cathay Pacific (which relocated from Hong Kong to Taipei in 1989), Korean Air Lines, Taiwan China Airlines and Asia Pacific Airways being the biggest international haulers and flag airlines. The country is still a heavy industry leader and the world's most adept high-tech manufacturer by a longshot.
(Russia's problems and China's continued isolation and poor relations mean that much heavy industry stays in Japan-Korea-Taiwan, and what goes to lower-eage countries first goes to the Phillippines, then Vietnam and Thailand, then Malaysia (which middle-income now) and Indonesia.
The Japanese Defense Forces were reformed in 1948, and grew with the country's status. After the Konfronstasi, the JDF grew dramatically as Japanese vessels began operating out of Kaoshiung, Taiwan, with the goal of protecting Japanese shipping and watching out for Chinese moves. Several skirmishes, including a near naval war with Indonesia in 1965 and the battle between Chinese naval units and JDF vessels in June 1989 have proved the JDF's defensive ability. Japan is not allowed to have an offensive military, but this is taken only medium seriously.
The flagship is JDF Asia, the former IJN Musashi, the only Japanese battleship to survive WWII. The battleship spent most of the 1940s and 1950s active, largely as a symbol of power of the unified navy. Retired in 1960, it was stationed as a museum ship in Kyoto until recalled in 1980. Originally just going to be used for show-off purposes, the Navy did rebuild the huge battleship as a flagship, with it returning to service in 1985. Asia is the only nuclear-powered ship of the JDF.
The Navy operates the second largest fleet of Destroyers, the largest fleet of Frigates and Corvettes and the third-largest submarine fleet in the world. Ranked third in world defense budgets, the nation largely relies on its awesomely powerful Navy and Air Force, as well as its highly-trained Marines. It's Army component gets usually less focus than the other branches, simply due to the Geography of the nation. Unable to build nuclear ships until Asia defied that boundary in 1985, Japan is the world's unquestioned leader in SSK development. The Mitsubishi F-14 Obake (Ghost in Japanese IIRC) is perhaps the world's most advanced fighter jet. Japan's own defense industry has been very advanced and able to make world-class equipment since the 1960s. The Kawanishi K112 Nightwatch is the natural rival, though the K112 is a ground-attacker whereas the F-14 is meant as a multi-role fighter.