That's a big room! How far away are you sitting from the TV and your sound bar?
The normal way that speakers are spec'd out, what you will see is an efficiency rating of something like 86dB / 1 Watt / 1 meter. In your case, your soundbar appears to be rated at 92dB / 1 Watt / 1 meter. I'm going to go ahead and assume that's the normal marketing BS that's used with most soundbars. They're probably playing all three channels at once, and probably only at a single frequency of 1 kHz in order to get that reading. So the REAL efficiency is probably closer to 86dB / 1 Watt / 1 meter, which would be typical.
So, what that means is that if you are listening to that soundbar from a distance of only 1 meter (roughly 3 feet away), it only takes 1 Watt of power to generate (supposedly 92dB), I'm guessing 86dB of sound output.
Every time you double your distance from the speaker, the output drops by 6dB if you're in a wide open field. In a real room, it drops more like 3 or 4 dB every time you double your distance.
Every time you double the number of Watts being used by the speaker, the output goes up by 3dB. And if you increase the Wattage 10x , you get a 10 dB increase in output.
So basically, you can calculate exactly how many Watts you need in order to get the loudness of output that you want at your seating distance. We just need to know that distance
Basically, I would assume that your soundbar can produce a maximum of about 106-109dB from 1 meter away, using the maximum amount of power that the soundbar can handle (listed as 175 Watts). The soundbar is probably distorting like crazy and begging uncle at that sort of output level, but it's only meant for short peaks of output, like a big explosion, or a sudden crescendo in music.
If you're 12 feet away, that's roughly 4 meters, which would mean that you've doubled your distance, and then doubled it again. That means the output would be somewhere in the range of 6-8dB quieter than if you were just 1 meter away. So I'm guessing the loudest your soundbar can possibly play (if you're 12 feet away) is about 100dB, which is very loud, but not hitting the 105dB peaks of "reference volume".
"Normal" listening levels are only about 75dB though. 85dB is "loud". And 95dB is "very loud". So it doesn't take a lot of Watts to hit those typical loudness levels. Even being somewhat conservative, from 12 feet away, it only takes about 1 Watt per channel to play at 75dB with your soundbar. And only about 10 Watts per channel to play at around 85dB. 100 Watts per channel should let you hit 95dB. And like I say, I'm guessing your soundbar will start to scream uncle if you try to play it much louder than that
You might be farther away than 12 feet though, given your room size. So the power requirements and limits of your soundbar's output start to increase dramatically as you move farther away.
So you might want to consider a speaker upgrade at some point. More efficient, higher output, higher power handling speakers that can really handle your large room size. And you could
definitely use a big subwoofer upgrade. A pair of really high output subwoofers, like some Rythmik FV15HP or something wouldn't be out of line in a room size such as yours. But that's only if you want to genuinely hit "reference level" with its 115dB peaks in the LFE and low bass
For now, a receiver that can genuinely deliver 100 Watts/ channel (which means the peak output will be higher) should be able to drive your soundbar literally as loud as it can go.
Since it looks as though you're aiming to keep the cost down a bit, the model I'd recommend to you would be a fully authorized, refurbished (still comes with a full 1 year warranty, no 90 day warranty BS
)
Onkyo TX-NR709 from accessories4less
The big reason why I'd recommend that specific model is because it is the least expensive (by quite a margin) AVR that includes full pre-outs for all speaker channels. Having those pre-outs means that you can add separate, higher power amplification in the future if you want to. If you get some higher output, higher power handling speakers in the future, you're gonna want some big, beefy amplification to go along with them. So the TX-NR709 will allow you to add that separate amplification in the future, whereas there are no other receivers at this $450 price point or lower that will allow you to do that!
The 709 also has some nice features, such as THX Select2 Plus and Audyssey MultEQ XT, which give you some really nice listening modes and some really great room EQ and auto-setup that you don't often find at this price point either.
For now, the 709 can power your soundbar literally as loud as it can go, so no worries there
Hope that helps!
