By using 41.8 SHP/ton machinery, I got what I wanted

I was able to design a 36-knot British light cruiser, to be laid down in 1923, that could reach 36 knots. The concept is rather like the Japanese fast light cruisers from the 1920's, except that this design has 9-6in guns, with three in superfiring positions. The protection is pretty meager, but that seems to be what is required to achieve such a high speed, with adequate composite strength and seakeeping. This is the Springsharp report:

GB/CL/1923, Great Britain Light Cruiser laid down 1923 (Engine 1950)

Displacement:
 7,882 t light; 8,164 t standard; 8,700 t normal; 9,129 t full load

Dimensions: Length overall / water x beam x draught
 598.89 ft / 595.00 ft x 56.00 ft x 20.00 ft (normal load)
 182.54 m / 181.36 m x 17.07 m  x 6.10 m

Armament:
      9 - 6.00" / 152 mm guns in single mounts, 108.00lbs / 48.99kg shells, 1923 Model
   Breech loading guns in deck mounts with hoists
   on centreline ends, majority forward, 3 raised mounts - superfiring
      4 - 4.70" / 119 mm guns in single mounts, 51.91lbs / 23.55kg shells, 1923 Model
   Anti-aircraft guns in deck mounts 
   on side, all amidships
      24 - 1.57" / 40.0 mm guns (6x4 guns), 1.95lbs / 0.89kg shells, 1923 Model
   Breech loading guns in deck mounts 
   on side, evenly spread
 Weight of broadside 1,227 lbs / 556 kg
 Shells per gun, main battery: 150
 6 - 21.0" / 533.4 mm above water torpedoes

Armour:
   - Belts:  Width (max) Length (avg)  Height (avg)
 Main: 2.00" / 51 mm 490.00 ft / 149.35 m 12.00 ft / 3.66 m
 Ends: Unarmoured
   Main Belt covers 127 % of normal length

   - Gun armour: Face (max) Other gunhouse (avg) Barbette/hoist (max)
 Main: 3.00" / 76 mm       -   3.00" / 76 mm

   - Armour deck: 1.50" / 38 mm, Conning tower: 3.00" / 76 mm

Machinery:
 Oil fired boilers, steam turbines, 
 Geared drive, 4 shafts, 121,185 shp / 90,404 Kw = 36.00 kts
 Range 5,200nm at 15.00 kts
 Bunker at max displacement = 964 tons

Complement:
 449 - 585

Cost:
 £2.358 million / $9.432 million

Distribution of weights at normal displacement:
 Armament: 153 tons, 1.8 %
 Armour: 1,192 tons, 13.7 %
    - Belts: 470 tons, 5.4 %
    - Torpedo bulkhead: 0 tons, 0.0 %
    - Armament: 102 tons, 1.2 %
    - Armour Deck: 593 tons, 6.8 %
    - Conning Tower: 27 tons, 0.3 %
 Machinery: 2,899 tons, 33.3 %
 Hull, fittings & equipment: 3,638 tons, 41.8 %
 Fuel, ammunition & stores: 818 tons, 9.4 %
 Miscellaneous weights: 0 tons, 0.0 %

Overall survivability and seakeeping ability:
 Survivability (Non-critical penetrating hits needed to sink ship):
   8,031 lbs / 3,643 Kg = 74.4 x 6.0 " / 152 mm shells or 1.1 torpedoes
 Stability (Unstable if below 1.00): 1.24
 Metacentric height 3.1 ft / 0.9 m
 Roll period: 13.3 seconds
 Steadiness - As gun platform (Average = 50 %): 54 %
   - Recoil effect (Restricted arc if above 1.00): 0.38
 Seaboat quality  (Average = 1.00): 1.09

Hull form characteristics:
 Hull has rise forward of midbreak
 Block coefficient: 0.457
 Length to Beam Ratio: 10.63 : 1
 'Natural speed' for length: 24.39 kts
 Power going to wave formation at top speed: 60 %
 Trim (Max stability = 0, Max steadiness = 100): 50
 Bow angle (Positive = bow angles forward): 4.00 degrees
 Stern overhang: 2.00 ft / 0.61 m
 Freeboard (% = measuring location as a percentage of overall length):
    - Stem:  27.00 ft / 8.23 m
    - Forecastle (20 %): 23.00 ft / 7.01 m
    - Mid (67 %):  23.00 ft / 7.01 m (15.00 ft / 4.57 m aft of break)
    - Quarterdeck (15 %): 15.00 ft / 4.57 m
    - Stern:  15.00 ft / 4.57 m
    - Average freeboard: 20.68 ft / 6.30 m

Ship space, strength and comments:
 Space - Hull below water (magazines/engines, low = better): 121.8 %
  - Above water (accommodation/working, high = better): 165.1 %
 Waterplane Area: 21,376 Square feet or 1,986 Square metres
 Displacement factor (Displacement / loading): 106 %
 Structure weight / hull surface area: 97 lbs/sq ft or 473 Kg/sq metre
 Hull strength (Relative):
  - Cross-sectional: 0.94
  - Longitudinal: 1.72
  - Overall: 1.00
 Hull space for machinery, storage, compartmentation is cramped
 Room for accommodation and workspaces is excellent