Luckily these ships were never engaged in battle by a hostile force, as they certainly had no defence against a modern weapon, other than four small CIWS's. Had the Cold War become a Hot War, these ships would have been facing terrible odds, against which they simply were not designed for.
And that is not all their luck. The powder was getting older and more unstable, and we were still using it. The one that lost the turret to a explosion on a test is an interesting example. The powder exploded as it was being rammed into the breech mechanically. This indicates highly unstable powder since the ram has very low forces compared to what happens in a tube and it lacks the containment of pressure that allows what should be very stable artillery powder. The bag was probably unstable enough that it was at risk of exploding from something as simple as being dropped. If the bag had just exploded a minute or two earlier while being handled in the main powder magazine, it would have set off the magazine and likely other magazines. The ship would have split in half and we would have losses such as seen on the Hood or the Jutland BC's. It is not the 100 pounds of explosives that doomed these ships, but losing magazines to explosions.
Back in the day, I bought into the hype. But in retrospect, these ships should not have left mothballed status in the 1980's. And if they did, they should have nevered fired their main guns or even had the main powder and ammo magazines fired. Just imagine the political impact of one of these BB having an internal explosion in Desert Storm. Or simply having one blow up during Reagan's term. 2500 dead sailors is hard to explain. And the military knew how lucky they were. This is why the came up with the bizarre "gay sailor cover story" where they basically fabricated evidence in a desperate attempt to make it sabotage not bad powder (i.e. Admiral or Reagan incompetence). At a minimum, you need a full run to manufacture new powder and ammo. Probably requires you recalibrate some spare 16"/50 on test range, assuming we have those lying around.
I understand that many people believe the Reagan hype for bringing out the ships. They are beautiful ships in ways our modern ships can never be. I understand the marines would like to have ships with very large guns for land support. It is just when you try to translate either the desire for 16" land support to a practical ship, it has a lot of problems. Same with armoring ships. And this is not a new problem. It goes back a hundred years. As soon as a BB (pre-dreads) guns and armor was not seen as able to take main gun line combat, we start seeing them become barracks and transport ships. I look at this for my TL where Germany had to make the decision. Again, they quickly move to secondary reserve status and soon after that the scrap yard. So what kind of ships can you build that look like a BB.
1) Assuming around a 16" guns is actually best way to support marines, you get a monitor. Probably stats of around 10-15 knots, very shallow draft, armored versus land artillery (all or nothing scheme probably), and small crew. Probably you are taking a civilian shallow water oil drilling platform as a base for the concept of the design. A barrage that can put down legs into the mud to increase firing stability. And something that can go deep into a river mouth. Now would such a device in southern Iraq have helped that much? Kind of doubt it, but it is the closest to practical. Fighting the soviets? Probably worthless. If you want 16" guns in Germany, you would just install them on land. Monitors are for unexpected battles. Now maybe something like Vietnam, it would be a big help to have one of these attached to each Marine Division or RCT.
2) Armor. As others pointed out, the sensor have to be on the outside. So this one is hard, but I guess I could see some argument for the Marine command ships to have some armor. Or any ship designed to carry Marines close to shore. But I am not sure it is worth the weight.
3) Now it is too crazy to actually do, but I can see a combination of #1 and #2. Your "Regimental Marine Monitor with 3 16/50 guns" also has a small area to serve as the Marine RCT command headquarters as the Marines are getting established. Sure it would be mocked, but it comes closer to a workable idea than any WW2 era BB running around or a new BBN/BBGN built in the 1980's. Unless someone builds a gun with a range of several hundred miles and can self guide to a target with sensors in the gun shell, we will never see a ship with guns as it main weapon again. There is work on making a rail gun, but since it is not even on the ships being built but will be a retrofit (maybe), it is clearly not the main armament.