Having reviewed my battleship books In order to capture the variety of capital ships in service in WW2, I believe we need:
Pre-Dreadnoughts
Schlesien & Schleswig Holstein (Germany), Sverige, Drottningen Victoria, Gustaf V (Sweden), Kilkis (& Lemnos) (Greece)
The Greek pre-Dreadnoughts were a training ship & hulk respectively by the time WW2 started, but the Kilkis at least could have been brought back into active service. Both were sunk by German dive bombers in April 1941.
Dreadnoughts
Alimirante Latorre (Chile), Minas Gerais (Brazil), Rivadavia & Moreno (Argentina), Yavuz Sultan Selim (Turkey), Jamie I & Espana (Spain), Marat, Parizhkaya Kommuna & Oktyabrskaya Revolyutsiya (USSR), Caio Duilio, Andrea Doria, Conte di Cavour & Giulio Cesare (Italy), Paris, Courbet, Ocean, Bretagne, Provence & Lorraine (France), Arkansas (US)
Super Dreadnoughts (WW1 Battleships)
Queen Elizabeth & R classes & Hood (UK), Fuso, Kongo, Ise & Nagato classes (Japan), New York, Nevada, Pennsylvania & New Mexico classes (US), Scharnhorst class (Germany), Dunkerque class (France)
Washington Treaty Battleships
Nelson class (UK), Colorado class (US), Bismarck class (Germany), Richelieu class (France), Vittorio Veneto class (Italy)
London Treaty Battleships (WW2 Battleships)
King George V & Lion classes & Vanguard (UK), North Carolina, South Dakota & Iowa classes (US), Sovetskiy Soyuz class (USSR), H-39 class (Germany)
Super Heavy Battleships
Montana class (US), H-41 class (Germany), Yamato class (Japan)
Half a dozen pre-dreadnought class ships may not sound like enough to justify their own tech, but consider that there were only 2 super heavy battleships actually in service in WW2. There are also the monitors HMS Erebus & Terror, which with 2 x 15" guns each come close to matching the firepower of a pre-dreadnought, although they were very slow and lightly armoured.
The early side of this certainly makes sense, though I'd still be inclined to 'round up' for the pre-dreadnoughts and just call them all dreadnoughts, those this would help most aren't liable to be huge naval powers to being with. Here's what I'd propose.
Dreadnoughts as you describe them splits off into Super-Dreads and Battlecruisers
New Yorks and Nevadas would fit here due to firepower and speed deficiencies.
Super Dreadnoughts ( tier 2 )
Defining features, notable improvements in speed, firepower and combat range but a fair bit more expensive
Queen E defines this class, Ise, the Pennsylvania to Tennessee classes fit here nicely
WWI Battlecruiser ( tier 2 )
Defining features, very fast, lots of firepower, poorly protected
Kongo, 'Splended cats', Hood
Washington Treaty Battleships ( tier 3 )
Defining features much improved vertical protection, mild improvements elsewhere, mild cost increase
Nelsons, Colorados, Nagatos
Washington Treaty Battlecruisers ( tier 3 )
Defining feature, notably better protection, notably expensive
Hood if it got the deck armor promised
Fast battleship 1934 ( tier 4, unifies battlecruisers and battleships into a single tree )
Defining feature, much more speed, mild improvements to firepower and armor, AA firepower can start to be powerful here without refits.
KGV, Bismark
Fast battleship 1939 ( tier 5 )
Defining feature, mild improvements in all main categories, AA firepower is much improved, somewhat more expensive.
SoDak, North Carolinas, Lion class, Iowas would be an improved variant ( as they were essentially stretched SoDaks )
Heavy Battleship 1939 ( tier 5)
Defining features, large improvements in firepower and armor, AA firepower is much improved much more expensive
Yamato ( while they didn't have the AA firepower it's hard to imagine poor AA as being a defining feature of this type of ship so much as being due to the issues with Japanese AA )
The ships that you list that I omit aren't meant to be excluded simply moved with their peers into appropriate categories, the ships mentioned are either emblematic of the type of ship or ships that are hard to categorize that have to be interpreted into one type or another ( standard battleships mainly ).
