As I feared, the big issue with the Tillman Battleship IV-2 is recoil

If you don't mind too much using very lightweight machinery, I could make the Tillman Battleship IV-2 "work", except for the recoil issue. I am not sure how to deal with that. Normally, I would increase the beam, but that would be "cheating", as the whole premise was to fit through the Panama Canal. I accepted a somewhat greater draft than might have been previously acceptable, as that greatly helps. This ship is 975ft x 108ft x 35ft, with 15-18in/50 BLR and 16-6in/50 QF guns. The maxmimum belt is 18in and the deck is 5in. I used the Wells Brothers' Tillman Battleship page. Too bad that their image is just not quite good enough to read the small writing. This is the Springsharp report:

Tillman Battleship IV-2, United States Battleship laid down 1919 (Engine 1937)

Displacement:
 69,149 t light; 73,207 t standard; 79,502 t normal; 84,537 t full load

Dimensions: Length (overall / waterline) x beam x draught (normal/deep)
 (990.59 ft / 975.00 ft) x 108.00 ft x (35.00 / 36.99 ft)
 (301.93 m / 297.18 m) x 32.92 m  x (10.67 / 11.27 m)

Armament:
      15 - 18.00" / 457 mm 50.0 cal guns - 3,086.99lbs / 1,400.24kg shells, 90 per gun
   Breech loading guns in turret on barbette mounts , 1919 Model
   5 x Triple mounts on centreline ends, majority forward
  2 raised mounts - superfiring
   Main guns limited to end-on fire
      16 - 6.00" / 152 mm 50.0 cal guns - 114.33lbs / 51.86kg shells, 150 per gun
   Quick firing guns in casemate mounts , 1919 Model
   16 x Single mounts on sides, evenly spread
  12 raised mounts
  4 hull mounts in casemates- Limited use in heavy seas
 Weight of broadside 48,134 lbs / 48,134 kg

Armour:
   - Belts:  Width (max) Length (avg)  Height (avg)
 Main: 10.0" / 254 mm 650.00 ft / 198.12 m 8.00 ft / 2.44 m
 Ends: 5.00" / 127 mm 250.00 ft / 76.20 m 16.00 ft / 4.88 m
   75.00 ft / 22.86 m Unarmoured ends
 Upper: 18.0" / 457 mm 650.00 ft / 198.12 m 8.00 ft / 2.44 m
   Main Belt covers 103 % of normal length

   - Torpedo Bulkhead:
  5.00" / 127 mm 650.00 ft / 198.12 m 33.00 ft / 10.06 m

   - Gun armour: Face (max) Other gunhouse (avg) Barbette/hoist (max)
 Main: 18.0" / 457 mm 9.00" / 229 mm  15.0" / 381 mm
 2nd: 5.00" / 127 mm 2.00" / 51 mm  5.00" / 127 mm

   - Armour deck: 5.00" / 127 mm, Conning tower: 18.00" / 457 mm

Machinery:
 Oil fired boilers, steam turbines, 
 Electric cruising motors plus geared drives, 4 shafts, 118,088 shp / 88,094 Kw = 25.50 kts
 Range 14,500nm at 15.00 kts
 Bunker at max displacement = 11,331 tons

Complement:
 2,366 - 3,077

Cost:
 £16.948 million / $67.794 million

Distribution of weights at normal displacement:
 Armament: 8,303 tons, 10.4 %
 Armour: 27,864 tons, 35.0 %
    - Belts: 6,895 tons, 8.7 %
    - Torpedo bulkhead: 3,968 tons, 5.0 %
    - Armament: 8,091 tons, 10.2 %
    - Armour Deck: 8,193 tons, 10.3 %
    - Conning Tower: 717 tons, 0.9 %
 Machinery: 3,273 tons, 4.1 %
 Hull, fittings & equipment: 32,191 tons, 40.5 %
 Fuel, ammunition & stores: 10,353 tons, 13.0 %
 Miscellaneous weights: 0 tons, 0.0 %

Overall survivability and seakeeping ability:
 Survivability (Non-critical penetrating hits needed to sink ship):
   108,574 lbs / 49,248 Kg = 37.2 x 18.0 " / 457 mm shells or 17.5 torpedoes
 Stability (Unstable if below 1.00): 1.01
 Metacentric height 5.8 ft / 1.8 m
 Roll period: 18.9 seconds
 Steadiness - As gun platform (Average = 50 %): 51 %
   - Recoil effect (Restricted arc if above 1.00): 1.71
 Seaboat quality  (Average = 1.00): 1.27

Hull form characteristics:
 Hull has a flush deck,
   a straight bulbous bow and a cruiser stern
 Block coefficient (normal/deep): 0.755 / 0.760
 Length to Beam Ratio: 9.03 : 1
 'Natural speed' for length: 31.22 kts
 Power going to wave formation at top speed: 40 %
 Trim (Max stability = 0, Max steadiness = 100): 40
 Bow angle (Positive = bow angles forward): 30.00 degrees
 Stern overhang: -5.00 ft / -1.52 m
 Freeboard (% = length of deck as a percentage of waterline length):
    Fore end,  Aft end
    - Forecastle: 20.00 %,  27.00 ft / 8.23 m,  27.00 ft / 8.23 m
    - Forward deck: 30.00 %,  27.00 ft / 8.23 m,  27.00 ft / 8.23 m
    - Aft deck: 35.00 %,  27.00 ft / 8.23 m,  27.00 ft / 8.23 m
    - Quarter deck: 15.00 %,  27.00 ft / 8.23 m,  27.00 ft / 8.23 m
    - Average freeboard:  27.00 ft / 8.23 m
 Ship tends to be wet forward

Ship space, strength and comments:
 Space - Hull below water (magazines/engines, low = better): 84.0 %
  - Above water (accommodation/working, high = better): 192.5 %
 Waterplane Area: 88,573 Square feet or 8,229 Square metres
 Displacement factor (Displacement / loading): 98 %
 Structure weight / hull surface area: 259 lbs/sq ft or 1,263 Kg/sq metre
 Hull strength (Relative):
  - Cross-sectional: 1.02
  - Longitudinal: 0.99
  - Overall: 1.00
 Hull space for machinery, storage, compartmentation is adequate
 Room for accommodation and workspaces is excellent
 Good seaboat, rides out heavy weather easily