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?

Your system suggests you would appreciate the sophistication of an OB/Dipole sub. A very unique one is available as a joint venture between GR Research and Rythmik Audio. The sub is not a normal Open Baffle sub, which are already unique enough, but an OB in an H-Frame, superior to a flat baffle because of it’s greater structural stiffness and non-resonance. And of course it’s open baffle design prevents the often boomy sound of even the best sealed subs.

A dipole sub excites the room modes of it’s front and back output, but not those of the room dimension to it’s sides, where there is a dipole null. There are a few OB/Dipole subs available, but the GR Research/Rythmik is unique in that the two (or three) 12" woofers (facing in opposite directions in the H-Frame) are Servo-controlled by the Rythmik plate amp. The amp also contains a 6dB/octave shelving circuit to offset the dipole front-to-back cancellation at very low frequencies.

The sub is offered as a kit only (one kit includes the amp and two---normally, though you can use three---12" woofers). The H-frame into which the kit is installed is available as an easily-assembled flat pack from a couple of wood workers who frequent the AudioCircle GR Research Forum. A pair of kits (for two subs) runs about $1500 shipped, and the flat pack (CNC cut from 1.5" MDF!) about $600. The highest sound quality, though not quantity, sub available.

Details of the design available on the GR Research and Rythmik Audio websites, and discussion of the sub on the Forum.

IMHO Servo flat plate amps and dedicated Open Baffle drivers naturally offer near flat bass response and do away with with nearly all the problems box subs cause as well as NEVER sound right. NO box sub can compete with a well made servo amp and 2 16 ohm 12" drivers for example. Or bigger or smaller for that matter. I like the 12's. 

I have the luxury of owning several systems and one of which has two Revel Rhythm2 subwoofers in it paired with Salon2's as well as all the goodies it needs to sound great and it's pretty good. Should be for $42K worth of speakers too however my GR RESEARCH Super V's I built (with those dual 12" drivers designed to go with these  by Rhythmic Audio's are sweet and simple as hell. They are the 370 PEQ  flat plate amp per side (I think they are called.  (thats a mere 370 watts vs. Revel's 2000 watts of blah blah blah BS is what it is.) the Super V's sound so much better in fact and without all the fancy dancy room correction LFO blahdie blahdie  blah digital crapola either, not even the onboard EQ switched on and dialed in eithe and it sounds 100 times better in every way with no nothing, no DSP, no room correction no nothin. I mean don't try messing up a room, but the room doesn't matter whereas with all other subs only the room matters. It's got to be darn near perfect and nobodies room is perfect ever.  For what, pennies in comparison too. In fact the sub's are for sale as are the Salon2. Who need this stuff when my kit speakers (on board subs) absolutely cream this other set up. It's kinda embarrassing frankly but live and learn. It's sad when you absolutely dial a super speaker and great subs in with super perfectly matched amps with super duper cables designed to extract the very best out of your room with that Synergistic Research Mojo KOOL AID crap too that works ever so incrementally it's sickening and more expensive the taking wonder trip around the world probably about 20 times or more. Simply all KOOL AID folks like all the other stuff. What a boatload, truck full, desert of KOOL AID. We don't need those ULTRA expensive cables either. What a complete smorgasbord of KOOL AID for the guzzling. I've finally learned. DO NOT DRINK ANY of it and keep your hard earned money. I truly hope I stop drinking that dam KOOL AID is all I can say because as always less is more and always will be. I"m serious about selling off this so called great Revel speakers too if anyone is interested. The Salon2 is a fine speaker actually as are the subs. I'll sell at my cost too. Got a bunch of stuff for sale actually, some super kool stuff too. Whoops I got off track here. So Sorry. I am serious about the sub's however, don't waste your money on much else I can honestly say. No JL, no REL, no Revel if you want absolutely killer sound that is or real sounding sound that actually helps your mains sound the best they'll ever sound. Not the worse, so you just keep struggling and spending and drinking, something, like KOOL AID. Check out Servo amps and nice big drivers and you'll be glad you did. GR Research sells them as does Rhythmic Audio and a whole slew of others too I'm sure. For that matter buy some open baffle speakers while your at too and hear the dam music you've been trying hearing for so dam long. No all OB speakers are created equal but most will have you tapping your toes like never before and stop that frustrating feeling of being had all the time. NO MORE KOOL AID should be every person that wants a simple great life new chant. Thats not a plug either it's just an honest recommendation. I have no reason to give them business except I think the stuff is great and totally underestimated across the board. NO subwoofer is going to sound as musical as these puppies. God's honest truth too. An expert audio engineer could work for 1000 hours trying to EQ, Room Correct, Add Bass traps and you name it and it'll never sound as good as just turning on a pair of dual 12"'s driver by servo amps. Not even close. The amount of frustration saved is worth every cent of the cost and more. You'll actually be able to listen to your music opposed to fussing with the horrendous task of trying to crossover some sub with your mains whereas it's not even really possible in 99% of all rooms no matter what anyone says. Oh you'll get noise or sound but it'll be nothing like those servo amps plates and OB drivers. Is the end all. I don't know but it sure as hell beats beating one's head against the wall buying XLR, Single ended, short long cables bass traps DSP bulloney with no mustard and all that nonsense and software no one car run and special Mic's that are nonsense bluetooth thingamajigs' for what. NOTHING. Mark my words folks and try making your mains sound right. you won't no matter what anyone selling KOOL AID tells you, ever. Sorry for all the typo's and my scatterbrain ADHD blather but for what it's worth there might just be something to what I'm saying here.