Start by changing your secondaries. If it's mid-30s, a divided secondary is rather superflous. Use 8 turrets with 120/127mm instead, or something similar. It will save a lot of weight, and be much more effective.
That is a good advice. I was thinking the ship with that configuration in mind, but the charasteristics of the dual purpose Japanese Gun was a bit poor. My idea is to work with japanese guns (it's going to be build there) or guns already owned by the Argentina.
But "what a hell", there are not Corsairs in the Southamerica, in the 30's. Regarding the weight, is now in 37.000 tons. With this little change i guess it will be a true "treaty battleship".
Six guns in the main artillery will require very good FC. I would rather use a smaller gun, say eight 356 mm with super heavy shells, compromising for the smaller caliber with increased shell weight.
The Latorre is already using 356 mm. The plan was to engage it at high distance. Using superior range of weapons and the fact that his armor is WWI style. May be the japanese can make me 2 triple tower? whit the dual purpose secondary I already save a lot of weight.
After that, you should focus on speed. In the mid thirties a new-built battleship should have at least 26 knots in speed.
Springsharp said its natural speed is 26,8 knots.
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I'll come in with a wildcard. 2 main turrets forward with 3x 381mm/50 per turret. Secondaries amidships and aft amounting to 12x 152mm or 155mm in 4x triple mounts. AA in the form of 8-10 twins 100-120mm and then whatever smaller mounts you want. In a later refit I'd probably land the two secondary batteries and replace them a good number of 120-130mm singles and twins.
Another good idea, But most of the ship is already designed, including internal arrangement, it will be too hard to begun almost a new ship.