I think a Yamato's 16" of armor could absorb a full loadout of 30MM tungsten or DU rounds without significantly affecting the ship's seaworthiness, but it would certainly cut a destroyer right in half.
I am thinking of making a 40MM big brother to the Phalanx, you could probably rip a 10000 ton freighter or even a light cruiser in half with that.
I'm halfway done with the base, I need to add the steps and access panels. The middle section and the upper R2D2 part should be a piece of cake. The barrels and the barrel support structure I think will be the tricky part.
After the Phalanx is done, I will start on a rail gun. That would certainly perforate a Yamato like a piece of cardboard.