If as you say, neither China nor Russia wants another nuclear state in the region? Do they want to deal with them on their terms? (I have my theories here)
Addressing the issue of the US needing a reason to warmonger in the East China Sea, I think you are overlooking a couple things. Assuming the premise is correct, and we need trouble with NK: to play devil's advocate, attacking NK is actually one way to guarantee years if not decades of ramped up US military presence there. 1) Do you think that it would be a clean wipe, and two weeks later we'd pack our bags and go home? Have you been following US military conflicts in the past decades? No, we would have even more presence there to clean up and police. 2) This would, as you said, cause even more conflict with China/Russia in the area, meaning we would need
more military presence (to protect our friends S Korea and Japan) no less-- remember that China/Korea/Japan aren't very friendly toward each other historically.