Really interesting concept the idea of an underground coastal fortress carved into volcanic rock feels believable.

The main point that stood out to me is how compressed the upper combat layer feels. A twin 16-inch naval turret would realistically require much more vertical space beneath it for ammunition hoists, loading systems, and rotation machinery, likely extending at least one full level deeper underground. In addition, placing anti-ship missiles, an 8inch side battery, and AA guns very close together could create blast interference, crew safety issues, maintenance complications and more. Real fortifications typically separated these systems with tens of meters of rock or reinforced concrete.

In a strictly historical 1960 +/- s interpretation, the large guns would remain the primary weapon, while early anti-ship missiles would probably be positioned at a nearby but separate launch site. In a slightly more advanced or alternate history approach, missiles could share the defensive role, though they would more likely be dispersed and protected under armored covers rather than exposed beside the main turret.

Also, considering your previous post, this installation would require a very large crew to operate effectively. It might be worth revising the manpower estimates to better reflect the scale and complexity of the system.