I disagree here. Secrecy of these designs was of the utmost importance to the Japanese, in order for them to have the advantage when war with the US started. In addition, even though Japan withdrew from the Washington Treaty on it's own, it was still bound by the agreement in 1934 when the Yamatos were designed. Japan had to withdraw from the Treaty before it could officially start construction on the Yamato. This was the political aspect of the situation.
Even though Japan was still bound to the 5-5-3 guidelines of the 1923 Washington Treaty in 1934, it had no intentions of adhering to the Treaty, which it withdrew from in 1936. While Japan knew that it could not compete with the US and England in terms of number of hulls that it could build (once the treaty limitations were removed) they set out to build ships that were bigger and more powerful than what was in the US fleet at the time. The result was the Yamato, on which, design work had begun in 1934, 2 full years before Japan withdrew from the Treaty.
The US on the other hand, was still adhering (strictly) to the Treaty in 1936 when Japan (now viewed as the most likely threat) withdrew. The North Carolinas and SoDaks were post-treaty construction battleships, but were developed and designed about the same time as Yamato, in anticipation of the Treaty falling apart. So how could the Japanese have known about the Iowas, and built the Yamatos to counter them, if Yamato came before Iowa, and for that matter, North Carolina and SoDak? Until Japan withdrew from the treaty, the US had no way of mounting 9 16" guns on a 35,000 ton hull.
Iowas were not built as counters to the Yamatos in the specific sense. When Japan withdrew from the Washington Treaty in 1936, the US knew they (Japan) would immediately start construction on ships which were superior to the current treaty battleships. They didn't know to what level Japan would take their designs. Since the compromises made on the North Carolinas and SoDaks by the Washington Treaty were no longer required, the Navy developed the Iowas as an improved SoDak. Better armor protection, a longer hull for higher speeds and better sea-keeping, and better internal compartmentalization.
The guns, fire control radar, AA suites, and CIC set ups are virtually identical to ships already on the line (the SoDaks and North Carolinas). Yamato and Musashi were built with 18.1in. guns because Japan knew the US could not produce an effective 18-inch gun ship that could fit through the Panama Canal. If you want to consider the Montana Class into the equation, there's a ship that was clearly built to counter a specific threat, in this case, the Yamatos.
So design work commenced on the Iowas in 1936, with the first hull laid in 1940. Yamato was launched in 1940.
While in a general broad statement you can argue that Yamato was built to outclass Iowa or vice versa, there's room for argument if you only look at specific aspects of their construction and histories. When you start to add in things like when design work started, proposed changes by BuC&R and the Navy, and then look at the FY appropriations, it becomes quite apparent that neither side knew about the specifics of either class, but both knew that ships superior to the current treaty vessels were inevitable.
Jeff