food for thought:
China claims the territories of the Tibetans because the Yuan Dynasty had physical dominion over those lands (no other dynasty, other than perhaps the Qing, another non-Han invader dynasty, had definitive physical claims over those lands), yet it does not make the same claims over Mongolia or, and more relevant to this thread, the whole of the Korean peninsular... of course, the Yuan Dynasty is Mongolian in origin, so maybe Mongolia should make a claim over all those lands...
the only way for China to be rid of US troops on the Korean Peninsular would actually inversely be by removing NK gov and letting the two sides merge... removing the threat of NK would remove the American excuse to base US troops there, and the SK people, who aren't all that enamored with having US troops on their lands anyway, would ask for their removal...
a united Korea could actually swing towards the China sphere, as they have massive economic cooperation between the two sides, and both have territorial disputes as well as historic differences with Japan, the main US ally in North East Asia...