If a Battleship is required then I must turn to the argument of a very big ship that can withstand heavy punishment and can be able to outgun her enemies.
I don´t like the H-Class, but not for her size or any ideological adversion but because they are not ideal. The H-Class with 8 x 16" guns is not a good option because the Iowas are more or less their match and, in every way, Yamatos outgun them. And if we are talking about a 120,000 ton 20" gunned H-Class then we better have a warp drive and photon torpedoes. Nope. Let´s have some BB that can be build...
My ideal ship is more or less a combination of Yamato+Iowa+Bismarck.
1. 12 x 16" guns (4 triple turrets)
2. Armour: an upgrade of Bismarck´s but with more depth and lenght in their belt armour, stronger deck and turret armour.
3. No underwater torpedo tubes.
4. No diesel, nah, let´s have boilers with turbines
5. Four shafts in an arragement very similar to CVN Enterprise or Nimitz Class. She must be able to have some steering with her propellers.
6. Heavy, but very heavy, AA defense. Every space in her deck and superestructure MUST be filled with proper AA bateries. (let´s say, some sort of naval 88 mm?)
7. One funnel.
8. Catapults for... what? A couple of naval modified ME 109... That´s cool!
9. Very high and strong superestructure and redundant bridges.
10. It must be painted with Baltic Camo just because of the looks.
Displacement: around 65 to 70,000 tons.
Lenght: 885 ft. (270 meters)
Speed: 31 knots (that means 200,000 hp)
Well that´s it. Destroy it please...