If South Korea really want to end this thing, they should just offer a massive “buy out” to the North Korean leadership. Basically, set them (and their children) up for life. That’s probably what it would take. And it would be a lot cheaper than another war. They would probably have to spend lot of $$ rehabilitating the North as well. What West Germany went through with the East would pale in comparison to that undertaking, however.
China won’t let that happen if it ever were to become a possibility. Too much risk at the border. As you suggest, it would be a massive undertaking, monetarily as well as culturally and physically (infrastructure, basic housing, schools, etc.)