Well, starting with a big 15" 1300 Watt subwoofer is a good move with that kind of room size
The sheer amount of air that is capable of moving is mostly a challenge for the bass, since bass is omnidirectional and a subwoofer is just going to attempt to pressurize the entire open volume of air. A sub doesn't "know" where your "theater area" ends and the rest of the kitchen and dining and high ceilings begin
But let's put concerns about the bass aside for now. I'm going to guess you're sitting somewhere in the range of 12 to 15 feet away from your TV screen and front speakers with a room that size. Certainly, I can understand why your little 2-way bookshelf B&W speakers are having a hard time in a room that size with that kind of seating distance!
While the Integra 70.2 is a very nice unit and certainly no slouch, it's still just an Onkyo underneath the hood and capable of about - at most - 500 Watts of power across all channels at once, and about 180 Watts max into any one speaker individually. In a big room like yours, you're losing about 4dB in SPL for every doubling of distance. So assuming your distance is about 4-5 meters, you're looking at about 80-82dB output with 1 Watt at your seat. Something in that range. At max power, they'd be tapping out at 100-104dB, but they'd likely be screeching at that output level, so I'm guessing you never quite push them that hard, since they likely start to sound pretty bad before that point - maybe a little scary
So yeah, I'd say you're going to want 3 new speakers across the front - considerably larger speakers that are capable of handling significantly more amplifier power, plus a new amp to really pump the Wattage into them.
Keeping closer to your budget, and also sticking with the midrange clarity and slightly laid back top end that I assume you like with your B&W speakers, one good option might be the EMP Tek E55Ti Towers with the large E56Ci center plus an Emotiva XPA-3 amp to power them all. Realistically, the EMP towers and center are about equally efficient in terms of output with just 1 Watt, but with so much more surface area, they can move a lot more air than your current 2-way bookshelf speakers, and they can absorb a lot more power, which the XPA-3 can provide. You'll be looking at a good 6dB more output and dynamic headroom with the new speakers, which is nothing to sneeze at! That's at least 4x more power and subjectively about twice as loud. Plus in-room response might get you another 3dB or so, so as much as 9dB louder from EACH speaker vs. your current B&W setup. That should easily get you to movie theater reference levels, while keeping the overall sound signature fairly close to your B&W sound that you're used to. The EMPs will likely sound a tad more forward in the midrange than what you're used to, but overall, they won't sound drastically different, the way going to a horn-loaded speaker or a line array or compression tweeter would.
You're looking at about $1250 for the towers and center plus $700 for the Emotiva XPA-3, so you're right on budget for all 3 speakers plus the amp
If there's more money available, some alternatives to consider would be the Paradigm Monitor 7 series, with the Monitor 11 towers and the Center 3 being the appropriate choices in terms of output capabilities in that series. $1600/pair for the towers and $600 for the center there. And again, a separate amp to really let them stretch their legs would be in order. You'd be getting a noteably different sound character going from the B&W speakers to the Paradimg Monitor 7 speakers. The Paradigms will likely sound "duller" and more "lifeless" to you at first, given their almost ruler flat response as compared to the more "colored" response of the B&W speakers. Definitely something you'd have to get used to, but once you do, you might appreciate some of the more subtle details that you start to notice that were never apparent with your current speakers.
The Ascend Sierra Tower and Horizon Center (Sierra Tower Center) with the standard NrT tweeter would be champs. You're up to $2000/pair for the towers and another $1000 for the center though - and those are the least expensive "matte black" finish. Nicer finishes are a few hundred extra. Outstanding speakers though, and worth the extra dough, as finding better speakers takes you into exponentially higher price brackets.
If you're really after just sheer, loud output, it's almost impossible to top JTR speakers. But be warned, these are basically outdoor concert speakers made affordable for home consumers. They're huge, they're ugly, they're over $1000 a piece, but they can almost literally blow the doors off of your house if you like
Heck, they can practically blow the doors off your neighbor's houses too. They can get INSANELY loud.
Anywho, those are just some suggestions and options that should fit your needs and your budget - depending on how you want to dole your hard earned money out. Regardless, I'd suggest getting an amp to power any of these options. You'll want the 400 Watts of dynamic power for that extra 3dB of headroom for big peaks in movies and transients in music.
Hope that helps!
