I think you are mixing a lot of different bits together.......
You need to split the post war stuff out as its got very different drivers to the WWII stuff, ie general HMT budget cuts (Tigerfish) and questions of if you really care about making ships survivable if they are throwing NDBs at anything that moves and expect to die anyway in a full WWIII.
A lot of GB shock problems is simply that RN kept deliberately going for the cheap option ie one water main/aluminium superstructure (Falklands) or less backup lights/generators (pre WWII) to save cost as they needed numbers and could not afford to gold plat stuff.
You know, all of that is fair and historical, but it sure still does not explain why the RN did not do due diligence on end effectors (weapons) and sensors (all the stuff that steers the effectors) post WW II. TBF budgets and numbers did hurt, but I will tell you it still does not explain the cultural flip in the RN. Or maybe I am being too harsh a bit. No Navy as depleted as the RN was in 1982 and still able to mount the Falklands campaign can be said to have lost its gung-ho or its fighting expertise. I simply noted that in the RN culture there seems to be a sneer at the engineer as a part of "the club". You cannot ignore those guys or you are going to get hurt. And that part of RN culture has not changed much going clear back to the Sir George Tryon. In the USN, the problem has been that of continual complacency and arrogance. The WW II wakeup call lasted until about Vietnam, but as that generation of WW II combat officers who remembered how badly beaten the USN was continuously until 1944 (Atlantic and Pacific) and the needed attention to make sure things worked and that doctrine fit situation, went into retirement and the old sins returned.
I hope the new reformers have figured it out.
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So what do we think will happen in each case?
Let's unpack.
A pair of G3s V a pair of Kongos ...... hummmm tarted up 1914 BCs v a fast battleship isn't going to go well 85%-15% and only due to the escorts torps if at night. (G3 win)
That is an invalid assumption on several grounds. The G3s are not true fast battleships any more than the uprated Kongos are. Then you have to look at the expected scenarios. First you are up against Kido Butai or Japanese RIKKOs in 1942 as well as the SAG. No Japanese SAG fought without scout support or its air cover. Hate to say this, but if the RN naval aviation is not there, it is likely that the RN surface action group is going to wind up like Force Z or the ABDA SAG did at Java Sea. The Kongos are part of a Japanese naval combined arms team. Until you nix their air forces, the IJN have you cold.
Denmark Strait v B & PE, G3 is basically Nelson guns (or better due to less weight cutting) that killed Bismark in OTL and its got better protection and faster.... its two v one as PE is almost irrelevant so 90%-10% (G3 win)
A lot depends on who sees whom on radar and the vector merge. A great deal more depends on the ADMIRALS. Lancelot Holland had the Hood, and he had the not ready for battle PoW, so it is practical to say with a couple of G3s, it is 2 to 1. But then again, look at aspects and firing arcs and the RTL history of the likely naval artillery employed. Holland gets the boot for trying to close the range and get the Hood in close where her belt armor should have worked, but... he turned to bring after batteries to bear too late in what he knew was a 1 vs, 1 situation. (about 15 seconds too late). The G-3s in that case present a 12 gun on 8 solution, exactly the same as the PoW and Hood did and they, too, have to get close because I suspect that same defect in the armor scheme around the fore structure as Hood had will be present. Holland still has the same problem and he probably will try the same solution. Will he succeed? Depends. Rodney says "maybe". Let's look at Rodney.
The Rodney had to close to PBR to punch into Bismarck's belt and consistently hit. KGV during the same action ran into gun issues of her own reminiscent of PoW. So we have no guarantee that the G3 artillery will not have Nelson type issues, but we do have a guarantee they will not be KGV issues. I'll give it 60/40 RN with possible both G3s surviving. I sure would love destroyer support, though.
Java Sea with Mutsu and Nagato (I really think more like Amagis ITTL?) but anyway 9 v 16" and faster and much better protected..... much closer than Kongo maybe 70%-30% (G3 win)
Mutsu and Nagato were tough bears. Braindead Takagi in charge, I give the RN a clear win. Anyone else Japanese (like tough old Kurita?) and the G3s die. Comes down to the torpedoes and air scouting. Japanese ones nose wander a lot. British ones are straight runners, but lack punch and range. If we go Amagis (and the Nagato type rebuilds), then even with Braindead it is an IJN victory. They were the best in the world at night surface actions. They knew how to scout and maintain a tactical plot.
As CV AA escorts v OTL RN ships ie probably QEs or R&R, they are just if not faster and have more protection as well as space for more AA. (G3 win)
RN AAA was NTG. Nobody else had decent AAA until about late 1942 either (all aspect directors and a good MAB auto cannon). I can see Repulse and Renown as CTF escorts. The QEs are too slow. The G3s would have to work in at least 4 x 8 pom poms with all asp directors and I would like to see a 4.7 in the DP battery. Modernized that way, they would be decent bodyguard ships.
I simply do see any situation that a G3 is worse than OTL using out of date Hood/R&R/R/QEs or slow N&R as not much else was available and worked up in sufficient numbers especially in the decisive stages of the war at sea ie pre 43 when US shipyards are up to full flow.
One may realize that in the North Atlantic this holds true, but in the Med and in the IO in the RTL the RN needed no less than 9 BBs to cover RTL needs 1939-1942? With Home Fleet added that is 14 BBs total. If you give up 9 of that RTL lot to get 6 G3s (2 more than the 4 projected) you are going to fall one ocean short and things get very dicey even if you add 3 KGVs.
In the PacFLT there is no effective battleship support until August 1942. Insane Pye has 6 Standards, but those are stuck on the American west coast either being refitted or repaired after Pearl Harbor RTL. They won't be ready until March 1943. ITTL US fast battleship support, assuming SoDak 2.0 ITTL would be 6... probably Atlantic based as in RTL with the North Carolinas to cover RN shortfalls. Makes for an interesting what-if. I can see SoDaks running with a Wasp to Malta easily ITTL.
Hmm. SoDak 2.0 (1 or 2) with Brits as RTL and Wasp (Yorktown version.) vs Littorio and company and LW on a May Malta run 1942. I still don't like those odds at all. It should wind up exactly like it did, a fiasco.