How about a 1921-style British Battleship-Cruiser?

The obvious next step is to design a 1921-style British battleship-cruiser. We are almost required to have a 31-knot speed, so that and the 15in armour basis greatly increase the displacement. I wanted 9-16.5in guns as the main armament with the obligatory 16-6in QF guns in twin turrets. The AA armament is 6-4.7in AA and 32-40mm (2pdr) AA guns. This is the Springsharp report:

GB/BB/1921 Battleship-Cruiser, Great Britain Battleship-Cruiser laid down 1921

Displacement:
 53,730 t light; 56,108 t standard; 58,500 t normal; 60,414 t full load

Dimensions: Length overall / water x beam x draught
 865.00 ft / 865.00 ft x 108.00 ft x 33.00 ft (normal load)
 263.65 m / 263.65 m x 32.92 m  x 10.06 m

Armament:
      9 - 16.50" / 419 mm guns (3x3 guns), 2,425.00lbs / 1,099.96kg shells, 1921 Model
   Breech loading guns in turrets (on barbettes)
   on side ends, majority forward, 1 raised mount - superfiring
      16 - 6.00" / 152 mm guns (8x2 guns), 100.00lbs / 45.36kg shells, 1921 Model
   Quick firing guns in turrets (on barbettes)
   on side, all amidships, 4 raised mounts - superfiring
      6 - 4.70" / 119 mm guns in single mounts, 50.00lbs / 22.68kg shells, 1921 Model
   Anti-aircraft guns in deck mounts with hoists
   on side, evenly spread, all raised mounts
      32 - 1.57" / 40.0 mm guns (8x4 guns), 2.00lbs / 0.91kg shells, 1921 Model
   Anti-aircraft guns in deck mounts 
   on side, evenly spread
 Weight of broadside 23,789 lbs / 10,791 kg
 Shells per gun, main battery: 90

Armour:
   - Belts:  Width (max) Length (avg)  Height (avg)
 Main: 15.0" / 381 mm 565.00 ft / 172.21 m 17.00 ft / 5.18 m
 Ends: Unarmoured
   Main Belt covers 100 % of normal length

   - Torpedo Bulkhead:
  3.00" / 76 mm 565.00 ft / 172.21 m 32.00 ft / 9.75 m

   - Gun armour: Face (max) Other gunhouse (avg) Barbette/hoist (max)
 Main: 15.0" / 381 mm 11.0" / 279 mm  15.0" / 381 mm
 2nd: 6.00" / 152 mm 6.00" / 152 mm  6.00" / 152 mm
 3rd: 1.00" / 25 mm       -         -
 4th: 1.00" / 25 mm       -         -

   - Armour deck: 6.00" / 152 mm, Conning tower: 15.00" / 381 mm

Machinery:
 Oil fired boilers, steam turbines, 
 Geared drive, 4 shafts, 185,028 shp / 138,031 Kw = 31.00 kts
 Range 5,600nm at 15.00 kts
 Bunker at max displacement = 4,306 tons

Complement:
 1,880 - 2,445

Cost:
 £13.022 million / $52.088 million

Distribution of weights at normal displacement:
 Armament: 2,790 tons, 4.8 %
 Armour: 22,198 tons, 37.9 %
    - Belts: 6,166 tons, 10.5 %
    - Torpedo bulkhead: 2,007 tons, 3.4 %
    - Armament: 5,140 tons, 8.8 %
    - Armour Deck: 8,398 tons, 14.4 %
    - Conning Tower: 487 tons, 0.8 %
 Machinery: 6,371 tons, 10.9 %
 Hull, fittings & equipment: 22,370 tons, 38.2 %
 Fuel, ammunition & stores: 4,770 tons, 8.2 %
 Miscellaneous weights: 0 tons, 0.0 %

Overall survivability and seakeeping ability:
 Survivability (Non-critical penetrating hits needed to sink ship):
   80,466 lbs / 36,499 Kg = 35.8 x 16.5 " / 419 mm shells or 12.1 torpedoes
 Stability (Unstable if below 1.00): 1.09
 Metacentric height 6.6 ft / 2.0 m
 Roll period: 17.7 seconds
 Steadiness - As gun platform (Average = 50 %): 53 %
   - Recoil effect (Restricted arc if above 1.00): 0.76
 Seaboat quality  (Average = 1.00): 1.06

Hull form characteristics:
 Hull has a flush deck
   and transom stern
 Block coefficient: 0.664
 Length to Beam Ratio: 8.01 : 1
 'Natural speed' for length: 33.59 kts
 Power going to wave formation at top speed: 53 %
 Trim (Max stability = 0, Max steadiness = 100): 50
 Bow angle (Positive = bow angles forward): 0.00 degrees
 Stern overhang: 0.00 ft / 0.00 m
 Freeboard (% = measuring location as a percentage of overall length):
    - Stem:  34.00 ft / 10.36 m
    - Forecastle (20 %): 24.00 ft / 7.32 m
    - Mid (50 %):  24.00 ft / 7.32 m
    - Quarterdeck (15 %): 24.00 ft / 7.32 m
    - Stern:  24.00 ft / 7.32 m
    - Average freeboard: 24.80 ft / 7.56 m

Ship space, strength and comments:
 Space - Hull below water (magazines/engines, low = better): 87.8 %
  - Above water (accommodation/working, high = better): 184.0 %
 Waterplane Area: 75,656 Square feet or 7,029 Square metres
 Displacement factor (Displacement / loading): 102 %
 Structure weight / hull surface area: 219 lbs/sq ft or 1,068 Kg/sq metre
 Hull strength (Relative):
  - Cross-sectional: 1.00
  - Longitudinal: 1.13
  - Overall: 1.01
 Hull space for machinery, storage, compartmentation is adequate
 Room for accommodation and workspaces is excellent