Here is the little extra i talked about before, a little snip to show differences between the Amagi class battlecruisers and the Kii class battleship.
the first two ships of the Amagi class Battlecruisers, Amagi herself and Akagi, where laid down on december 6th and 16th 1920; by the time the other two, Atago and Takao, where started on november 22nd and december 19th 1921 smoke problems around the bridge where emerging from the trials of the Nagato class Battleships, so the project for the two late ships was revised with the introduction of trunked funnels in order to move the uptakes away from the bridge.
Those modifications where supposed to be implemented on the Kii class Battleships also, wich where ordered to the Kure, Yokosuka, Kobe and Nagasaki navy yards on october 16th 1921; the Kii class Battleships where basically an improved version of the Amagi class Battlecruiser with an 11.5-inch belt (compared to the 10-inch of the Amagis) and slighty lower top speed.
The drawing shows how the aforementioned modifications would have made the two late ships of the Amagi class beign more close in appearance to the Kii class Battleship ones than their two early sisters.