Finlandization is basically an American delusion. Between Finland and the Soviet Union, the latter was culturally, economically, and technologically decrepit and had nothing to offer the Finns. China, on the other hand, is technologically competitive, the second-largest economy in dollar terms, and is working on developing its soft power. If the Chinese don't screw up, a Sinocentric order in Asia is inevitable.
China and Korea, as a cultural entity, have no fundamental conflicts of interest. Chinese claims to Kogoryo are merely out of political expediency, and we can point to the Sino-Russian border treaties, as well as the ceding of Mongolia, to see how quickly the Chinese are willing to forget about territorial claims if they're politically expedient.