Reviewing the options I don’t see any reasonable way out other than accepting North Korea as a nuclear power, then invite them to the big-boy table and insist they play by the rules.
There are plenty of countries we tolerated going nuclear when we didn’t like it, going way back to the Soviet Union many decades ago. Deterrence, as in mutually assured destruction, has worked so far. In North Korea’s case it would be more like unilateral destruction — and it won’t be us. And that’s all we can do, have ever been able to do, ever since we “distinguished” ourselves as the only nation every to rain down a nuclear holocaust on an enemy.
Letting North Korea go nuclear isn’t ideal, but I don’t see an acceptable alternative.
On The Backend
For the long-term big picture, it seems overdue for the U.S. to seriously (and secretly) talk with China about a unified, peaceful and non-aligned Korean peninsula that sends Little Kim and South Korea’s corrupt government packing. This could be a good time to start anew on this question. China and the U.S. each would have to give up long held policies to get there, but surely this crisis demonstrates our combined self-interest in putting this ridiculous running gag of two Koreas behind us.