Perspective from a pro AV systems designer, long time AV and hifi hobbiest here.
Everything should be kept in balance. And with rooms/systems, balance is key. There are plenty of reasons that you should consider smaller speakers and a smaller sub combo in such a small space. Without going into all the details, the short version is that you should keep all the speakers in proportion to the size of the space, for best sonic (and visual lifestyle) integration. Short form, is that 5 to 7 small satalites, and medium sized sub, integrate much easier into that sized room than does 5/7 large monitors and a big sub!
A room that small doesn't properly support deep bass anyway, has limited bass absorption capabilities, and could use less bass energy, as a whole, because of that. Also, I recommend people steer towards piston type speakers with 5.25" drivers as a maximum, because they integrate better typically into the small room space, response wise (typically), and are less boomy overall. Basically, they just seem to sound more well balanced, when setup up right, in small spaces, exagerate lower bass modes, a bit less, usually offer better off-axis sound, yada yada.
Then, becuase you are going to cross the speakers over at 80hz, a smaller woofer tends to also cross over higher and integrate with satalites much better than larger counterpart woofers.
Bottom line, that 15" sub is much better suited to rooms that are at least twice as big as yours in my experience. And I really like that Paradigm sub! It's a terific tool. However, like any tool, it needs to be implemented in the right setting, in the right system and room. And I would not shell out $1200 for a monster sub in that small room. You don't need it.
I would much rather see you with something with a 10" woofer, and properly integrate it into the space. Dual 10" woofers even. And then you'll be EQ'ing the woofer ultimately, sure. Still, stay smaller woofers. A single is more than fine in this room. It will play hard and deep (enough)to do the job. No, it won't play down to 5hz. But then so what?! Balance and quality over quantity.
You won't be using anywhere near the potential of that large Paradigm, it will be way too much bass energy and boom for that space (you'll need to really EQ it hard. And even then, you'll have too much reverb energy down low, making the space sound too warm, thick, and sluggish and boomy in the bass).
Yes, go with something like the Paradigm PS1000 in that line, or similar. If you have to spend more on better subs, go small power-cubs with higher watts, Earthquake 8" or 10" models, Sunfires, and other small sealed woofers.
Lots of offerings from a near infinite amount of manufacturers. So do some research.
But, I vote NAY on the large Paradigm for now. It would be the equivalent of putting a 350cu inch blown chevy into a VW Bug! - you wouldn't do it.
Save that one for a larger space, and save some money!!!
Basically, I've been doing systems for decades now, and I wouldn't go Servo 15 in your small space - even though it's otherwise a superb (one of my fav's) woofer, on it's own.
Nope, wrong fit...