A simultaneous strategic + tactical nuclear strike with the intent of wiping out North Korea and it's conventional and nuclear forces would prevent the huge losses for the South.
Just keep our politicians out of the war. MacArthur was right; we should have defeated North Korea and we should have used nukes. Truman screwed up and was the first President to "kick the can down the road."
There's nothing in North Korea except the nuclear weaponry that they have developed that is worth saving/protecting. Other than scouting and gaining control of their nuclear material, there's no reason to commit troops in North Korea. In the ghastly aftermath we should round up their nuclear material and leave everyone to die, instigating expeditions only occasionally to see if we missed anything. No occupation is necessary; no nation-building.
Sometimes extreme measures are called for. Carthage was one example for Rome. Rome delayed too, and Carthage caused Rome great damage until Rome destroyed it. We should effectively "Salt the Earth." in North Korea.