My strategy would be:
* Land in Korea, to demolish their last industry, as Myth suggested. Free the Republic of Korea as a UN ally.
* ally with China
* land somewhere along the Chinese coast, preferably at a place where you can split the Japanese holdings in two, and then drive west to establish a corridor to link the Chinese with the coast. China is in terrible shape - you probably need to give them a hand, to help the Chinese get back on their feet (maybe liberate a few IC rich provinces for them) and then leave them to do the rest. Maybe they need help against their western and southern neighbours, though... particularly the Germans in the west... an expeditionary corps might be needed. You could mod the Chinese AI file to make them focus on annexing smaller Japanes puppets, and on getting their rich cores back.
* keep Japan occupied, until you have time to deal with them in detail - meanwhile, let them rot and have them get eaten by the Chinese.
* once the Japanese have lost China and Korea, you can manually trigger a surrender event - then you annex all that is left of Japan and can do as you wish with them. Manchuria would lose its puppet status and China can choose how best to deal with them. The Soviets and the Mongolians get their land back. You can then release Japan as a new puppet, but without their military.
I think the idea of a "republic of Japan" isn't that good. Firstly it would require a lot of modding, secondly it is extremely unrealistic. More likely, the US administer Japan militarily until the Japanese government kicks the bucket. It would also be unrealistic to assume that the US can simply walk away from a defeated Japan and leave the country to itself - no, even a defeated Japan still requires the US to keep forces in there. I guess you could lower the partisan level in the Japanese islands, though, to simulate that the demoralized Japanese get along alright with the occupiers. They did historically, and in here the emperor and the army are so badly disgraced that the home islands will refuse their calls for resistance to the occupiers.