So if we assume states able to perform at the level of the OTL Ming and Joseon present when Japan invaded, the results would likely be limited.
Therefor the crisis in at least China would need to be much worse, and would need to be unusually long. Perhaps not even a crisis, then, but another division of China following a crisis.
Basically, yes. The PoD itself would need to occur long before 1000, which would probably butterfly away the Liao, Song, Jin, Yuan, and Ming altogether.
Maybe not politically assimilated (until the 1900s), but certainly assimilated in an ethnic and cultural sense. Keep in mind that there were Han bannermen.
As for Japan establishing a dynasty in China, it seems that it would have to first create a solid presence in Korea by conquering it and totally extinguishing any native peninsular kingdom. This would happen sometimes towards the end of the Yuan dynasty in the 1300s. A couple hundred years later, Korea is solidly Japanese and the "Ming" is suffering from revolts, Mongols, and Manchus. The Ming collapses as IOTL, and the Japanese move in to snatch Manchuria and turn it into a vassal. With peace on the Yalu, some Manchu leader goes and tries to conquer China. He succeeds in taking North China and making peace with the Mongols, but is stopped around the Yangtze, with a "southern Ming" remaining. All this is happening in the late 1500s or early 1600s.
Goryeo was extremely militaristic throughout its existence, and it was probably only second to Goguryeo out of all Korean dynasties in terms of its emphasis on the military. In particular, although Gongmin managed to declare independence due to the Yuan's disintegration, he was able to consolidate his position due to various generals (specifically Choi Young and Yi Seong-gye) who had risen to prominence after repelling northern raids (Red Turban Rebellion), along with numerous wokou raids. The dynasty eventually collapsed because it was too expansionistic, as the court ordered General Yi to invade Liaodong in order to counter the Ming's claims on Goryeo's northern territories, as the state was still hyped from its successes against the Yuan. However, he eventually decided to retreat and stage a coup, as provoking China would have been suicidal, along with setting up a military dictatorship and executing Choi Young (despite showing deep respect for him) in order to avoid becoming branded as a traitor, and finally establishing Joseon in 1392.
As a result, a Japanese invasion of Goryeo might actually have resulted in a counterattack on the archipelago, which would have not gone well for both sides.