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Japan's whole strategic calculus was unbelievably unrealistic.

They were between a hard rock and a worst place prewar after we cut their steel and petroleum supplies.  Their generals in China would not have complied with any orders from Tokyo to pull back or "be nice".  They really were facing a very dire situation without gaining oil supplies (SE Asia).  And what lay between them and Indonesia/Borneo?

The PI.  

They figured/hoped that a sharp early serious reverse inflicted on the US would buy time, and perhaps lead to negotiations somehow.  This would probably mean US withdrawal from the PI so Japan could get oil from SE Asia and be "independent".  Yamamoto of course counciled against this, but they were in a bind.

I've toured it twice, a while back.  Obviously it's very similar to the South Dakota class, and you would look hard to distinguish it from the Iowa class really.  I didn't get why we had two classes at the same time so similar, I think it related to the naval treaty, but don't remember offhand.

I was speaking of the very similar classes of the North Carolina class (of which two were built) and the South Dakota class.

A number of deficiencies in the preceding North Carolinas were to be fixed in the South Dakotas; these included insufficient underwater protection and turbine engines not of the most recent technology. The North Carolinas also did not have sufficient space to act as fleet flagships, so the lead ship of the new class was designed with an extra deck on the conning tower specifically for this purpose, although the increase in space and weight from this necessitated removal of two twin 5-inch dual-purpose (DP) gun mounts.^[3]

I've toured it twice, a while back.  Obviously it's very similar to the South Dakota class, and you would look hard to distinguish it from the Iowa class really.  I didn't get why we had two classes at the same time so similar, I think it related to the naval treaty, but don't remember offhand.

It did. In accordance with the Treaty System based on the Washington (1922), London (1930), and Second London (1936) Naval Treaties there was a prolonged global pause in new Battleship and Battlecruiser construction.

Here are the final pre-pause Battleships/Battlecruisers for the US, Britain, and Japan:
United States:
The last pre-treaty Battleships of the USN were the Colorado Class ships. Four were planned and all four were launched before the treaty but one had to be scrapped to comply. The USN also had to convert two Lexington Class Battlecruisers then under construction into what became the Lexington Class Carriers Lexington and Saratoga. The Colorados had eight 16" guns, weighed ~32k tons, and had a top speed of 21kn. The Colorados were built 1917-1923.




Britain:
The last pre-treaty Battlecruiser of the RN was the Hood. Hood was originally to be one of four Admiral Class Battlecruisers but the other three were canceled due to lessons learned at Jutland and their replacements were never constructed due to the treaties. Hood had eight 15" guns, weighed ~45k tons, and had a top speed of 32kn. Hood was built 1916-1920.

The "Nelrods", Nelson and Rodney of the Nelson Class were the last pre-treaty Battleships of the RN. They had nine 16" guns (in an unusual all-forward layout), weighed 33k tons, and had a top speed of 23kn. The Nelrods were built 1922-1927.

Japan:
The last pre-treaty Battlecruisers of the IJN were the four ships of the Kongo Class. They had eight 14" guns, weighed ~27k tons, and had a top speed of 27.5kn. They were built 1911-1915.

The last pre-treaty Battleships of the IJN were the two ships of the Nagato Class. They had eight 16.1" guns, weighed ~33k tons, and had a top speed of 26.5kn. They were built 1911-1915.

Due to the treaties, no new Battleships or Battlecruisers were completed until the late 1930's in the run up to WWII. Hood was the largest warship in the world for 20 years.

After the pause the US built ten modern Battleships:

• 2 North Carolinas that more-or-less complied with the treaties (post-escalator clause)
• 4 South Dakotas that more-or-less complied with the treaties (post-escalator clause)
• 4 Iowas that were not limited by the treaties. Two more Iowas were nearly completed but never finished due to being surplus to late-war and postwar needs.

Britain built six:

• 5 KGV's that more-or-less complied with the treaties. One (PoW) was lost.
• 1 Vanguard completed after the war.

Japan built two:

• 2 Yamatos that were not limited by treaties. Both were lost and a third was completed as an aircraft carrier and also lost. The two completed as Battleships were the largest Battleships ever built and the aircraft carrier was the largest aircraft carrier ever built until the US built supercarriers much later.

I didn't recall that the two additional Iowas were nearly completed.  I think the Kentucky was laid down and construction had been halted maybe halfway, and the sixth might have been laid down and never really started beyond that.

I think you are correct and that the sixth was never started. However, the bow of the Kentucky was affixed to the Wisconsin after the Wisconsin had a ship to ship collision during sea trials, that severely damaged her bow. They brought it back into the Newport News ship yards, removed the newly completed bow from the Kentucky and replaced the damaged bow of the Wisconsin.

The USS Illinois just before being cancelled.  

German aircraft carrier Graf Zeppelin - Wikipedia

Speaking of major ships not completed, what a waste of resources this one was.   And of course the Japanese effort to convert a Yamato class to a carrier was less than successful as well (Shinano).

DVIDS - News - The Yokosuka-built Aircraft Carrier Shinano (dvidshub.net)

On Nov. 19, 1944, Shinano was officially commissioned, and on Nov. 28 departed for Kure, Yamaguchi prefecture, where the remainder of the ship-fitting work would take place. Shinano, with escort ships, had only been cruising four hours before they were caught on radar by the Balao-class submarine USS Archerfish (SS 311) and followed through the waters near Tokyo Bay.
Shinano’s escorts included the ships Isokaze, Yukikaze and Hamakaze, which were caught on Archerfish’s radar and followed by the submarine on a parallel course.
Believing that Archerfish was a decoy to lure Shinano into a convoy attack, Capt. Toshio Abe, commanding officer of Shinano, ordered that the ships outrun it by using a zigzag maneuver. However, by midnight, the ships were forced to reduce the speed to prevent the Shinano’s propeller shaft’s bearing from overheating.
Archerfish grabbed the opportunity and submerged in preparation for an attack. Shinano tried to turn southwest but ended up heading straight toward the submarine. Within a matter of minutes, the ship turned south, inadvertently exposing its side, offering an ideal firing situation for the submarine to attack.
At 3:15 a.m. Nov. 29, 1944, Archerfish fired six torpedoes, striking Shinano.
According to Hosokawa, Shinano was hit in the shaft-room of the #3 Engine Room on the starboard side. Upon impact, several thousand rivets on the bulkhead, especially between the shaft room and the engine room, came loose all at once. For IJN ships, rivets were used throughout the hull unlike modernized vessels, which are largely built by welding. The damage got worse with increasing water pressure and was beyond the crews’ ability to correct. Lifeboats and buoys were not available for the crew aboard Shinano, as they believed that, “escape from the ship equals timidity,” recalls Hosokawa.
Shinano was sunk on its maiden voyage 160 nautical miles southwest of Tokyo Bay, going down in history as the largest warship annihilated by any combatant submarine during World War II.