Yes, those B-52 "ARC LIGHT" missions won THAT war for us, didn't they? Strange how I managed to forget that... Your assumptions are correct, insofar as we will "win" any war with N. Korea (even if China should jump in- unlikely). But the death toll will be so high that you will think it's a misprint when you see it in your paper.
You might want to review the histroy of the Korean War, especially from 25 June 1950 until MacArthur managed to land at Inchon- we were routed- entire units broke and ran South, and Seoul was practically destroyed almost immediately. That was WITHOUT nuclear or chemical weapons.
That's right. ROK and US forces were pushed hard south until they held only a pocket that included the port city of Pusan. MacArthur backdoored the North Koreans by coming in behind them at Inchon, west of Seoul.
When the US retreat was at its most earnest, serious thought was given to employing tactical nukes against North Korean forces massed in pockets between some of the interior southern mountains of Korea.
Until Inchon, we were fighting a losing battle. Then when the Chinese stepped in, the game was destined to be lost.
Land wars in Asia usually end that way when Chinese armies get involved.