In the case of the two battleship actions, on both occasions, the Japanese were hampered by the shell loadout they were using. On both occasions they were loaded out with HE shels, which severely downgraded the effectiveness of their guns, at least initially. On both occasions they were not expecting the opposition they received,. In the second battle, despite being outnumbered, and outgunned, and at a tactical disadvantage, Kirishima still came close to sinking the sth Dakota, who suffered repeated failures. Washington was very fortunate, her radar allowed her to close to point blank range, and pump a full broadside into the japanese ship from point blank range. Even a bismarck or a new Jersey would not have withstood that sort of pounding.
It is true that South Dakota suffered numerous failures; radar, gun directors, radar plot and radios were shot out. Radio communication was out because all of the ship's antennas were shot off! But the main problem, electrical failure, was self induced and this left her main battery silent.
Until my brother came by, I had a book that listed the Japanese order of battle. So, from hazy recall I think there were 26 IJN ships in the waters around Guadalcanal that night. This includes some Marus on a mission to land troops on the island plus their escorts. In the immediate neighborhood of the battle there were:
Battle Crusier (I contend) Kirishima a 30 knot ship armed with 8x14inch, 16x6inch and 8x5inch guns
Heavy Cruiser Atago a 35 knot ship armed with 10x8inch guns
Heavy Cruiser Takao a 35 knot ship armed with 10x8inch guns
Light Cruiser Nagara a 36 knot ship armed with 7x5.5inch guns
Light Cruiser Sendai a 35 knot ship armed with 7x5.5inch guns
Plus seven destroyers
I point this out because this battle is often described as being between the Kirishima and the South Dakota or the Kirishima and the Washington when in fact there were 12 IJN vessels in the area.
So, as for Kirishima being outnumbered, I say false. As for being outgunned, that is a judgement call, does the many guns of the Japanese fleet rule or does the throw weight of the 16 inch rifles?
As for the contention that the bombardment group was hampered by being loaded out with HE shells, I agree. Of the heavy hits received by South Dakota, two were HE, two were Incendiary and only one was AP. The AP round struck the barbette of number 3 turret, misaligning the roller table and making the turret hard to train. South Dakota was also hit by what appears to be the cap head of a 14 inch AP round, the projectile having disassembled upon hitting the water.
You state Kirishima came close to sinking South Dakota. That got me wondering how good the shooting of the Kirishima was the night of her loss? According to the South Dakota damage assessment posted at
USS South Dakota Damage Analysis
the South Dakota was hit 27 times. Some of the hits are known to have come from the heavy cruisers, the Kirishima did not have 8 inch guns and South Dakota took five 8inch AP rounds and 2 8inch HE rounds. Tallied up, as best as I could (the source of some of the hits is unclear), it looks like the Kirishima was responsible for 14 or 15 of the hits, a little over half. You are welcome to make your own tally if you wish. So, this was an engagement between the South Dakota, the Kirishima, some cruisers and maybe IJN destoryers.
As for the South Dakota, she emerged pretty beat up but in no sense close to sinking and still making full power. One interesting thing was the hull seams that opened up well below where hits impacted her side armor. This I take to be the result of having side armor far inside of the outer hull. Another fact I came across was that the Washington was shooting nearly over the South Dakota to engage the Kirishima. Luckily, no holes in the other side of South Dakota.