PTT, What a silly idea that is. 300 warheads seems to indicate a forecast absence of a significant enemy state. In which case this organisation is hardly going to have the resources to find 1 SSBN, let alone an entire fleet. So why hold back? Just get rid of all the boomers except for the few required.
Also, what yield are these warheads likely to be? The existing <Megaton, lower 00Kiloton range, or higher >megaton yields more akin to Russian standards? Obviously having heavier weapons is a way to negate the effects of fewer weapons, but it leaves fewer options if a country did decide to start harvesting their mushrooms. How could you instigate a first strike with 300 small yield weapons? And if you wanted to retaliate, what damage could you seriously expect to deliver? Deterrent? Nope. Weapon? Barely better than a pea shooter against a serious enemy.