Japan 51 cm/45 (20.1") "A" Type 98 (?) - NavWeaps
The bursting charge of the 20 inch HE shell intended for the A-150 'Super Yamato' would have been 84kg. Not... hundreds of kg.
There are actual data and formulae on how much armor is required to defeat an HE shell.
Okun Resource - Miscellaneous Naval-Armor-Related Formulae - NavWeaps
This formula suggests that a 20 inch nose-fused HE shell could, at most, assuming a point blank impact at 90 degrees at 2300 fps (basically muzzle velocity), blow a 20 inch hole in a 6.8 inch plate of STS homogeneous armor, and that a 8.16 inch plate is the maximum thickness that would be cracked or dented. (Yes, I realize that the armor in the game would be face hardened, but I don't think it makes a huge difference here).
Based on this I would expect a 4.6 inch plate to end up with a ~30 inch hole. As for the 25 inch belt... I wouldn't expect any damage at all. This is generous as we're not talking about point blank, 90 degree impacts, this was an engagement at around 20 km where the shells would be striking much closer to 45 degrees and would been slowed by air drag.
There's a reason that AP was used - HE is just not very effective against heavy armor. If HE shells were able to cause significant, incapacitating damage to battleships without penetrating, battleships would have been built with very different armaments and protection schemes.
In no way should 11 20 inch HE partial penetrations (several of which hit the strongest part of the protection scheme - a protection scheme far stronger than any ever constructed) be able to put a 75,000 ton battleship in serious danger of sinking due to structural damage. Battleship protection schemes were designed to protect propulsion, steering, the main armament, ammunition, and enough reserve buoyancy to keep the ship from sinking from anything short of an AP shell, AP bomb, or torpedo that was actually powerful enough to penetrate.
From HE shells, I would expect damage to the less armored areas, and a superstructure hit to seriously mess up fire control and spotting, but currently in the game, you can *sink* a battleship with HE without ever penetrating its armor. There is no way that is reasonable.