Best type of Sub to consider?

Kenny: I'll share my thoughts, though I don't know your main speaker (which, I gather is a modified Lowther-type driver augmented with woofers and depends on corner reinforcement):
1. If I had to choose between a coherent speaker that was optimized for its full range vs adding on subwoofers to augment the bass, I'd probably do everything I could first to optimize rather than add. I know you said you have no options, but looking at that room, the side facing the system looks like it has "corners" (I assume there are windows behind the blinds, so you might have to deal w/ inserting some kind of rigid panel behind the "corner" blinds when listening). Perhaps with cabling, power outlets and the like, it's too much of a pain.
2. The notion of feeding the woofer amp from your main amp isn't crazy- my Avantgardes are set up that way and though their woofers are driven by their own internal solid state amp, the thinking is that they take on the behavior of the main amp feeding them (in my case, a SET amp).  The cables to do this made a difference- I went through various "jumpers" before I arrived at one that sounded better than the others.
3. The woofer design may be less important than placement and dialing in- read some of the other threads here- about swarm woofers, about dipole kits to match the behavior of panels. 
4. I've been messing with subwoofers for a long time for music and was never happy, having had various Quad loudspeakers (electrostats) and then horns. (I didn't even bother trying to sub-woofer my Avantgardes until quite recently). Right now, I am achieving some improvement using an unmatched pair of subs, crossed low, no roll off of the main woofers, and have been fiddling with DSP. I didn't want the discontinuity typically associated with subs and planars or horns, and didn't want to muddy the midrange. I've managed to get it 'just so'- more foundation without screwing up the mids---
5. Your system looks like it came from Jeff at High Water, who has very good ears, and is a cool guy. Even if he doesn't sell subs, does he have any advice for you?

George has passed, but there is probably a good mastering suite in heaven. 

Interesting. Just for additional background, I bought a 12 inch sealed unit from Brian at Rythmik recently, opted for the paper, rather than metal cone, and for cosmetics, had it finished in that piano ebony gloss (which may not look right with your aesthetic). I got the version of the plate amp with XLRs that allow me to daisy chain (which I'm not doing right now). The other woofer I'm using is a very old Velodyne 15" to which I added a small DSP unit, and cross it over really low. I am running the pair in stereo, adjusted to match the output of the 4 x 10" woofer array in my Avantgarde Duos. I am not rolling off the main speaker system through any external X-over, but running the subwoofers parallel to the main system from additional outputs on the back of my line stage. Although, as described, it is sounds a bit kludged together (and it is), it has worked very effectively. So, the idea of using two different sized subs isn't completely crazy. (I have another old sub, a Velodyne 18", which I didn't bring into the room- it's about the size and weight of a fully loaded coffin and it just seemed to be too much, and unnecessary). I am using the set up described as a stop-gap until I move and rebuild the system, where I'll revisit the whole speaker array. (Bigger horns, please!)  The bigger woofer sits further back into the room, behind the "line" of the main speakers and off in a corner; the Rhythmik is closer to my listening position on the other side of the room at a "jog" in the room so it has some "corner loading" but it is more mid-wall, if that makes any sense. Using some pretty simple tools, including a db meter, some of the basic measurement tools that come with that Studio Six app for iPad as well as my ears, I was able to adjust the volume, crossover and phase in a way that pretty harmoniously adds weight, depth and gives me more of a front to back effect without doing violence to the glorious midrange of the X-overless mid horn and SET amps.
For what it's worth, my dealings with Rhythmik were very pleasant, Brian was responsive to my questions via email and phone, and the fit and finish, as well as the performance of the 12" woofer is pretty impressive for the $. So I guess you could call that an endorsement.

Thanks, bdp. I know when I ordered the 12" from them in paper  cone that I looked at 15" versions, but I'm probably not going to invest in more woofers or subs (than I already have) until I move and reassess the speaker system as a whole. 

BDP- does Rhythmik make a sealed 15" sub with a paper rather than metal cone? When I looked at their site a while ago, I thought the 15" were all metal coned- but may be wrong.