You have not sent me a link to your current sub.  If you can send me a link or exact details of your current sub I can render an opinion.  Just because a driver is larger does not mean it has to be a better sub, in equivalent applications.
You still have not sent me a link to your current driver and box.  I can't find any details of that 12 inch driver you quoted.  However here is another 12 in Dayton sub I modeled previously.  There are no xmax problems and the F3 is 17 Hz.  The spl is a little lower than yours above 50 Hz, 111db versus 114db.  However it maintains that spl to 20 Hz, where your 15 drops to 102 db.
Name: Dayton TIT320C-12
  Type: Standard one-way driver
  Company: Dayton
  No. of Drivers = 1
  Fs =  22.2 Hz
  Qms =  6.12
  Vas =  73.91 liters
  Cms =  0.0977 mm/N
  Mms =  525.8 g
  Rms =  11.98 kg/s
  Xmax =  18.7 mm
  Xmech =  28.05 mm
  P-Dia =  304.8 mm
  Sd =  729.7 sq.cm
  P-Vd =  1.364 liters
  Qes =  0.47
  Re =  3.07 ohms
  Le =  3.17 mH
  Z =  4 ohms
  BL =  21.89 Tm
  Pe =  500 watts
  Qts =  0.44
  no =  0.166 %
  1-W SPL =  84.35 dB
  2.83-V SPL =  88.6 dB
-----------------------------------------
Box Properties
  Name: 
  Type: Vented Box
  Shape: Prism, square (optimum)
  Vb =  4.303 cu.ft
  Fb =  17.28 Hz
  QL =  6.283
  F3 =  18.18 Hz
  Fill = minimal
  No. of Vents = 2
    Vent shape = round
    Vent ends = two flared
    Dv =  3 in
    Lv =  28.27 in