Advice on replacing 12 in woofer in Martin Logan Monolith III's

So the box is not square as George indicated, it is 25 inches wide and tapers to 19 inches at rear.  24 inches H and 11 inches deep

@stevepa    
Ok,  assuming a 1 inch front baffle and 3/4 inch everywhere else, you're looking at 2.469 cubic ft... so if we model on 2 1/2 cubic ft, we'll get accurate results.

I have many time added mass to raise qts so that a woofer would go down better in sealed box.

Adding mass to the cone does lower the FS, but you didn't mention it also raises the distortion (slows down it's reaction time) at the higher end of the woofers capabilities.
You give to one end but take away from the other, there's no free lunch.

Because it's such an odd trapezoidal type of shape, I'm positive when I bean bagged filled the bass chamber to do a proper volume check, it was more than 2.5cu ft.

Cheers George

stevepa

Just listen to the Eminence ones till you get some SV-12's, two of us, Jon Fo and I both looked for a replacement for a very long time and the SV-12 was the one.
  
Jon Fo later did raise the xover point to some 300hz? to take away some of the power frequencies from the ML esl, and then used the Peerless 830699 for bass/mid/upper bass but I think he then used big external subwoofers as well to make up for the Peerless no being able to go down.

Cheers George    

Sorry George, Not sure where all of your info comes from, but adding mass in alone does not add distortion... In fact if the mass is a stiffener, depending on cone, it could decrease it.
@stevepa    Steve,  George and I could take you down 2 different roads.  To be fair to George, I do not have his direct experience with your speakers, but in fairness to me,  I come from a back ground of driver and speaker design.  I speak from experience and an understanding of how all of this comes together. 
 The good news is that I do agree, that a good sealed woofer is the way to go.  I have not found one that is really a great match for your Monoliths.... On the other hand, I have found 1 Dayton Pro, that would work very well indeed if you would be willing to port. It would be a very viable alternative.  It seems George is questioning your measurements,  if they are correct, you are at 2.5 cu ft.... Bean bags would decrease it. 
  I hope all of this helps,  Tim