It seems to me that the real point of NKs efforts to have nukes that can reach US territory is to give them enough time when they launch an invasion of South Korea for it to be fait accompli - fact on the ground - before the US intervenes.
In other words, up until now, if NK forces crossed the DMZ, the US immediately starts massacring those forces with conventional weapons. However, if NK has a few icbms with nukes that can reach US territory - even just Guam - the US will hesitate until it knows those missiles have been neutralized. Thus, the US would spend the first part looking for the missile launching sites to take them out. Only after the US has satisfied itself that the icbm threat is neutralized will the US be willing to start attacking NK's invasion force with conventional weapons.
My guess is that the NK plan is for that to take sufficiently long that it will be firmly in control of Seoul and enough of SK that the US will simply have to accept the invasion as accomplished, because - I'm sure the NK also believes this - the US is not going to be willing to launch an open-ended campaign of attrition to extirpate NK invasion forces once they're dug in over a significant portion of the South.
I think that's really what NK wants its nukes and icbms for. They aren't first and foremost interested in actually attacking the US.