Hi, I've been searching for subs as well although I had no where near your budget except for the Klipsch R-112SW.
I had a 24 year old Velodyne CT-100 sub that died. It was a 10" woofer, front slot ported, subwoofer with 100 watts rms/250 watts peak power. It had a frequency range of 28Hz - 120Hz +/- 3db.
I can say that it didn't sound anywhere near as good as my current Klipsch R-120SW that I bought. The Klipsch is much better for music. I hear detail that I never heard with the Velodyne plus the Klipsch has more punch.
The Klipsch R-120SW has a 12" woofer, rear round port with 200 watts rms/400 watts peak. It has a frequency response of 29Hz - 120Hz =/- 3db.
I am space limited also so I couldn't have some monster subwoofer.
My Velodyne CT-100 size including grill and volume knobs/heat sink was 16.5" tall, 15" wide, and 18.5" deep. The new Klipsch R-120SW is 16.5" tall, 14" wide, and 19.75" deep.
Both subs are about the same size even though the Klipsch has a 12" woofer. They both have nearly the same frequency response. As far as bass extension, they both sound about the same in bass extension although the Klipsch may go a bit deeper.
I originally tried Jamo sub and Polks Flagship sub but they didn't work out for me. The Klipsch subs were much better.
I bought the Klipsch R-12SWi at Costco for cheap at $279. It's in the same model year as the R-112SW and shares the same finish. That finish is BAD. The laminate is a cheap plastic wrap. Just moving the sub around, I scratched it. It scratches very very easily and is a very cheaply made finish. I returned it based on that alone but found that the newer R-120SW that replaced it now has a scratch resistant wood pattern vinyl type laminate. Still not the greatest as my current Polk TL1600 subs and Velodyne sub but much better. It also has a different woofer and sound much better. It's more accurate where the R-12SWi emphasized the upper bass to much and more detailed or tighter. It was a very significant difference when placing subs in the same position, leveling volume with a Radio Shack Level Meter. The R-120SW is $20 more, and without wireless capability but well worth it for the better finish and better sound quality IMO.
So beware on the Finish of the R-112SW. I'd honestly look at the new Klipsch SPL-120 which is only $100 more.
For me, the Klipsch SPL-120 was to big for my space and the Monster sized SVS PB-1000 Pro wouldn't come close to fitting. I thought about the SVS PB-1000 but only was being sold by one dealer who I had an issue with and SVS wasn't selling it at the time. It was actually to big for my space as well but entertained the idea.
SVS just started selling it again for some reason at it's original price of $500 after I bought my R-120SW. I put the PB-1000 out of consideration when I read of several forum posts complaining of clanking and noise issues with the sub. I don't want a trouble sub and for the cheap price SVS is selling this, I have to wonder what corners were cut to get price that low for it's bass extension and output. After seeing the posts complaining about noise, it struck me that's where the cost savings went.
The smaller 10" Klipsch R-100SW sound really good but with less bass extension as the R-120SW. It goes pretty low and it's small, nearly as small as my Polk TL1600 8" subwoofer it replaced in my media room. Sounds excellent.
Sounds like you have a much bigger budget than me so you should be able to get a loud, small sub with deep bass extension as many brands offer this at a premium price.
BTW, my living room is 16' X 15' X 8' and my listening position from the TV/main speakers is 13' and 14' from subwoofer behind the front right main speaker.
My system goes low, below 30Hz. I hear 30Hz pretty strong. It goes even below that into the mid 20s where I can feel it! Youtube reviewer charted his in room frequency response and he was getting -3db around 28Hz and -6db around 25 Hz. Even -6db is good output that you will feel. My hearing doesn't go below 25 Hz but I can say that this R-120SW has excellent bass extension and does great for Home Theater. The Klipsch SPL-120 should go about 3 or 4 Hz even lower. I wouldn't pay more than $500 for the Klipsch SPL-120 though.