But the third Yamato (Shinano) went down with just 4 submarine torpedo hits.

The Shinano's demise had a lot to do with stupidity and circumstance. Not all of her watertight doors had been installed. The ship's compartments hadn't been tested for water tightness and most of her crew was untrained with a good percentage of them being civilian dockyard workers still helping fit the vessel out. Plus, Capt Abe insisting on proceeding at speed despite the torpedo hits judging the damage inconsequential. Rather than face the embarrassment he went down with the ship. Fearing the impact on national morale, the sinking was concealed from the Japanese people until after the war.

All true,and the fact that she was completed as a CV,not a BB. Different subdivision,avgas storages tanks probably empty.

There was also a weak spot in the Yamato class armor where the torpedo blister met the rest of the hull. The Archerfish's torpedoes all hit this spot.