The SVS SB13-Plus is a great, sealed sub, but it just isn't well suited to the sort of large, open space that you have. As with virtually all sealed subs, the SB13-Plus starts to roll off its frequency response fairly high - around 40-45Hz. It is a shallow 2nd order roll off, thanks to the sealed design. So in a small, enclosed room, the boundary effects and room acoustics will boost that lowest octave of bass so that the overall frequency response is something closer to flat. But in a larger room such as yours that also has openings to other spaces, you're not going to get those bass reinforcement effects from the room itself, and you'd be left with something closer to the subwoofer's natural rolled off frequency response, which is less than ideal.
So, with your space considerations in mind, I would recommend getting a ported sub that can play nice and flat down to 20Hz or lower all on its own, as well as provide more output than a similarly priced sealed sub and be more efficient.
With your $1000 desired budget, it is unlikely that an SVSound sub will meet your needs and budget. The PC12-Plus DSP cylinder is $1300 delivered and the PB12-Plus DSP box is $1350 delivered, so at least a few hundred dollars over your budget. That said, if you can stretch your budget that far, you won't find better performance or a more sophisticated amp in the same price range. If you can swing $1300-$1350, I can 100% recommend an SVS "Plus" ported subwoofer.
Looking for something closer to your desired budget though, my next choice would certainly be Rythmik. When you want your stated combination of deep, powerful bass along with highly accurate, tight, controlled sound, Rythmik certainly fits the bill! Their ported subs are excellent.
Once again, going over budget, at $1200 + $120 shipping, the FV15HP is extremely close in terms of overall performance to the SVS PB12-Plus DSP. Of course, once you include shipping, it's also almost exactly the same price!
Right now, Rythmik is having a bit of an issue with parts supply. The flooding and other natural disasters in Asia has led to parts shortages for a lot of companies. As a result, many of Rythmik's models are on back order with no known shipping date for the foreseeable future.
The slightly less powerful FV15 doesn't have a "back order" flag on it at the moment on Rythmik's website, but I'd give them a phone call to check on stock, just to be careful. At $1050 + $120 shipping, the FV12 is closer to your budget while giving up only around 3dB of output across the board.
After SVSound and Rythmik, I'd look to HSU and Outlaw Audio (the Outlaw subs were made with substantial input about the design from Dr. Hsu).
I am not personally a fan of the HSU VTF-15H. In my own listening, it is my least favorite HSU sub that I have ever heard. So while it might claim the most output, it's not the sub that I would recommend. It just didn't have the same sound quality that I am used to from HSU/Outlaw subs. My experience in listening didn't line up exactly with the measurements that Audioholics posted in their review, but my overall feeling that it isn't HSU's best sub is shared. What I heard didn't sound as linear as the measurements that Audioholics got. I was hearing more of a hump in the 40Hz range as well as a fair amount of overhang and distortion in the lowest bass octave. To my ear, it just seemed as though the amp wasn't powerful enough to handle the lowest bass. I don't know. The VTF-15H certainly has some very vocal fans. But it isn't my top choice.
So I'm going to recommend the VTF-3 MK4, but with the caveat that I've only heard the VTF-3 MK3 in person. I am assuming though that the MK4 version won't be massively worse than the MK3 version for some odd reason though
The Outlaw LFM-1EX is a sister model to the VTF-3 MK3. So you can get a rough idea of the VTF-3's performance from the Audioholics review of the Outlaw LFM-1EX. The sound won't be completely identical, since the driver orientation and port location are different. But the components and overall design are largely the same. So it's a good "ballpark" idea of what you'd be getting.
I like HSU's VTF-3 MK3 a lot. As I said, I'd expect the VTF-3 MK4 to be very similar. It's got HSU's trademark clean and accurate sound. None of the bloated or overhang-laiden bass that plagues other reasonably priced ported subs. While HSU uses "off the shelf" parts at lower price points, he wrangles very good performance out of those parts with very good engineering and design.
Bottom line, if you want to stay under that $1000 budget, for your room, the HSU VTF-3 MK4 or Outlaw LFM-1EX is the way I would go! I personally think that the SVSound PB12-Plus DSP or PC12-Plus DSP cylinder is noticeably better, but it's also nearly twice the price and well over your budget. If you have the freedom to optimally place your subwoofers, you could almost get two of the VTF-3 MK4 or LFM-1EX for the same price!
Regardless, for your room size and environment with openings to other rooms, I would strongly recommend that you go with a ported sub in your situation. Between your original choices of the SVS SB13-Plus and HSU VTF-3 MK4, I would recommend the VTF-3 MK4 more highly for your setup. If you CAN stretch your budget, it is possible to get a subwoofer that is even a bit better in the Rythmik 15" ported subs or the SVSound "Plus" ported subs. But for under $1000, the VTF-3 MK4 or Outlaw LFM-1 EX are the way to go, IMO.
Hope that helps!
