In my mind there are two kinds of scouting. The first is you know roughly where the enemy is and you want to watch them (eg shadowing or vectored by other means such as aerial recon or radio interception) and the second is where you don't know where the enemy is (eg hunt for the Graf Spee type operations).
The latter requires good range more than speed and for this a CL is likely to be superior but when you know the enemy is close and your following an enemy force the DD scout has more speed to dash to safety and is less visible. Don't forget the smaller destroyer type scout will cruise at economical speeds, only in emergencies and combat will full speed be used.
3000 tons sounds viable, to gain seakeeping simply extend the forecastle deck further back or have a flush deck design.
Here is a quick attempt I've done my taking a G Class destroyer and increasing the freeboard and length and adding extra bunkerage. The results are not too bad (especially seakeeping).
Light Scout, Great Britain Scout Destroyer laid down 1936
Displacement:
2,667 t light; 2,784 t standard; 3,192 t normal; 3,519 t full load
Dimensions: Length overall / water x beam x draught
429.10 ft / 420.00 ft x 34.00 ft x 16.00 ft (normal load)
130.79 m / 128.02 m x 10.36 m x 4.88 m
Armament:
8 - 4.50" / 114 mm guns (4x2 guns), 45.00lbs / 20.41kg shells, 1935 Model
Quick firing guns in deck mounts with hoists
on centreline ends, evenly spread, 2 raised mounts - superfiring
4 - 1.57" / 40.0 mm guns (1x4 guns), 2.00lbs / 0.91kg shells, 1922 Model
Anti-aircraft guns in deck mount
on centreline amidships, all raised guns - superfiring
12 - 0.66" / 16.8 mm guns (2x6 guns), 0.14lbs / 0.06kg shells, 1935 Model
Machine guns in deck mounts
on side, all forward, all raised mounts - superfiring
Weight of broadside 370 lbs / 168 kg
Shells per gun, main battery: 250
8 - 24.5" / 622.3 mm above water torpedoes
Armour:
- Gun armour: Face (max) Other gunhouse (avg) Barbette/hoist (max)
Main: 1.00" / 25 mm 0.50" / 13 mm 0.50" / 13 mm
2nd: 0.50" / 13 mm - -
3rd: 0.50" / 13 mm - -
Machinery:
Oil fired boilers, steam turbines,
Geared drive, 2 shafts, 52,254 shp / 38,981 Kw = 34.00 kts
Range 6,000nm at 16.00 kts
Bunker at max displacement = 736 tons
Complement:
212 - 276
Cost:
£1.757 million / $7.027 million
Distribution of weights at normal displacement:
Armament: 47 tons, 1.5 %
Armour: 17 tons, 0.5 %
- Belts: 0 tons, 0.0 %
- Torpedo bulkhead: 0 tons, 0.0 %
- Armament: 17 tons, 0.5 %
- Armour Deck: 0 tons, 0.0 %
- Conning Tower: 0 tons, 0.0 %
Machinery: 1,433 tons, 44.9 %
Hull, fittings & equipment: 1,091 tons, 34.2 %
Fuel, ammunition & stores: 525 tons, 16.4 %
Miscellaneous weights: 80 tons, 2.5 %
Overall survivability and seakeeping ability:
Survivability (Non-critical penetrating hits needed to sink ship):
1,274 lbs / 578 Kg = 28.0 x 4.5 " / 114 mm shells or 0.4 torpedoes
Stability (Unstable if below 1.00): 1.28
Metacentric height 1.5 ft / 0.5 m
Roll period: 11.5 seconds
Steadiness - As gun platform (Average = 50 %): 50 %
- Recoil effect (Restricted arc if above 1.00): 0.75
Seaboat quality (Average = 1.00): 1.91
Hull form characteristics:
Hull has a flush deck
and transom stern
Block coefficient: 0.489
Length to Beam Ratio: 12.35 : 1
'Natural speed' for length: 23.05 kts
Power going to wave formation at top speed: 64 %
Trim (Max stability = 0, Max steadiness = 100): 26
Bow angle (Positive = bow angles forward): 20.00 degrees
Stern overhang: 0.00 ft / 0.00 m
Freeboard (% = measuring location as a percentage of overall length):
- Stem: 25.00 ft / 7.62 m
- Forecastle (20 %): 21.50 ft / 6.55 m
- Mid (42 %): 21.00 ft / 6.40 m
- Quarterdeck (15 %): 21.00 ft / 6.40 m
- Stern: 21.00 ft / 6.40 m
- Average freeboard: 21.44 ft / 6.53 m
Ship space, strength and comments:
Space - Hull below water (magazines/engines, low = better): 159.7 %
- Above water (accommodation/working, high = better): 88.0 %
Waterplane Area: 9,794 Square feet or 910 Square metres
Displacement factor (Displacement / loading): 94 %
Structure weight / hull surface area: 39 lbs/sq ft or 192 Kg/sq metre
Hull strength (Relative):
- Cross-sectional: 0.50
- Longitudinal: 4.87
- Overall: 0.63
Hull space for machinery, storage, compartmentation is cramped
Room for accommodation and workspaces is cramped
Excellent seaboat, comfortable, can fire her guns in the heaviest weather
Misc weight includes:
ASDIC
Full load DCs (two racks and four throwers)
4 reload torpedoes and handling gear