Having made a few of those SSBN patrols, I would be the first to say that this is definitely case for strategic deterrence.
Especially if it were to prevent the deaths of millions in Seoul, who are the balance in this little game of blackmail.
Kim keeps jumping up and down screaming that "this" is an act of war or "that" is an act of war. It's time to call his bluff (but with a baseball bat in tow just in case).
The US and Japan had better start giving serious consideration to a complete naval blockade of North Korea while simultaneously issuing a joint statement via a press conference that ANY North Korean provocation against ANY of its neighbors will be viewed as an attack against the United States and Japan and that such an attack will be met with deliberate and overwhleming retalitory force. End of statement - no questions, no follow-ups. Just let the concept sink in with the NKs for a few minutes. Within minutes, China will be calling 'ol Kimmie to tell him to knock the crap off or THEY will go in after him.
Left unchecked or left to fetter under the United Nations, the NKs will succeed in their nuclear blackmail. Right now, they can rain death upon Seoul within minutes. They need to understand, however, that doing so will result in the utter destruction of both the "dear leader" and all of North Korea as they know it. This reality check needs to be done publicly.
Today.