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

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

@stevepa   
If you are up for it,  Jon Fo's idea for George is not bad either to raise the crossover point,  The Good, removing the mid bass (100 - 300hz)  off the panel, cleans up the mids and make for cleaner midrange.... The Bad is that you have a crossover point in the vocal region. 
Its a trade off, but easy enough to do if interested.
Also,  I have looked for this, but have not found it... the best single woofer that I know of for your application is an Tonegen 1259, also known as NHT 1259... Madisound had done a close copy called the Madisound 1259... so if you are looking around for the SV12, You could add this to your search... Good Luck,  Tim

Sorry Tim but you clearly have no experience with mating esl’s which are very fast (low mass) compared to a dynamic drivers (much higher mass), as there are big problems at the xover point to get them to seamlessly sound coherent and it is an art to get them to do so. A low FS for LF, and a low MMS for speed at the xover point is a good place to just to start, this is why the SV12 is an ideal choice.

Adding mass to a driver just to get it to go down further will create problems up higher exacerbating the problem where this xover point is most critical to have both esl and driver sounding/blending well to be coherent.

Over here a Monolith I (ported) sounds worse in the (above area) and is reflected in it’s used value around $3k.
A Monolith III (sealed) used fetches between $10k-$12K why would anyone want to port this and "maybe" get a worse sound.

BTW: Bean bag (pellet) fill (beans being the operative word) will give you an exact volume measurement of that weird shaped enclosure, as it takes everything inside the enclosure into account.
I hope your not thinking, leaving the fill in there as stuffing??? As that would be stupid. It’s a precise measuring tool, then to be taken out and put into a symmetrical container to work out the correct volume of the Monoliths weird shape enclosure volume.

Cheers George

If you do raise the xover point to 300hz you get the problem that many speakers have of having two drivers doing the critical midrange. This is even much more accentuated with ESL’s.

This is why a Monolith with a 150hz xover sounds so much better in the critical midrange than a ML Summit with a 300hz xover. The reason Jon Fo went this way is because he uses 4 x Monoliths with external subs is for HT use with all that processing and that critical midrange xover in HT is not as big a problem than just hi-end stereo use.

Cheers George

"Sorry Tim but you clearly have no experience with mating esl’s"

But what I do have is a knowledge of how it works and why.  I do understand blending panels and a woofer...
I know that you guys don't know me from anyone, but when Sumo designed the Aria speaker, they did call me for advice and way back when,  The very company that you are speaking of Martin Logan did call me and ask me to come interview with them... which I declined. 
I'm old and I've been involved in speaker design since I was 19. So rather that turning this worst and telling you what you don't know, I will bow out....
@stevepa can easily private message me if he needs help.