US positions...
I figure the US will not go any closer to the Chinese border, and may even pull out entirely (lessen tensions between China, SK and US) but keep a naval presence, partly as backup since no one else has a "true" blue water navy, and to reassure US comittment (and nuclear umbrella) to the area. Perhaps even pull out of Okinawa...
My preference for taking out NK is China decapitates the leadership, NK/SK join. China gets preferential business rights, US "donates" $50-60 billion in aid for at least 10 years.
Or, my half baked invasion scheme:
US attempts to bribe colonels and generals to defect or do nothing if attacked. Even a few hours would be critical. Only criteria is our spies can get in and out safely; no need to give NK propaganda coups. If they find out we are bribing, so much the better: they purge, reinforcing our story tis better to bribe than die. A great SecState is needed, to shuttle between China, Russia, Japan, and SK.
As much as I prefer a sneak attack, we will have to demand 30 days to turn over any nuclear devices or war. If they don't, fight like Desert Storm I, with aerial assault for a few weeks. Most of the US and Japanese navy have to be stationed nearby to shoot down any missiles. Above all, treat the enemy with respect, ie they can kill you if you let them. As the US appoaches the Yalu, China swarms across the river. No, really. One, to remind the world they are a power. 2, the keep hundred of thousands of refugees out of China. P-town (can't spell it) will be a bear to take, but maybe China can negotiate a peace.
End result is China gets first rights on minerals, US withdraws out of Okinawa and SK to show not trying to crowd China (fleet still stops by Japan), NK tries to set a goal of reunification in 10-25 years. The above countries all promise a total of $100 billion in aid until reunification (like other foreign aid, loan/give money to a country then make that country buy from you!).
Japan has no nuclear threat, so I can't see any differences. SK is tough, and can stand on her own, but may loosely ally with Russia (least chance of domination compared to China/Japan). China I bet would prefer a split Korea, but at least this way they can import cheap, and sell machinery/steel, plus making the US leave the China Sea. US gets the ship NK stole from them a few decades ago. Might even justify cancelling a Ford carrier or two...