The best speaker for a small room...at any price point.

Size of room is one thing, but how close are you sitting to the speakers? How far are the speakers from the wall behind them? Ported speakers don’t perform well in small rooms, so you might want to try plugging the ports if equipped and plugging is supported. I’d recommend near field monitors. Yamaha makes very nice near field monitors - HS5 and HS8 with an available active subwoofer with crossover. 

I have a pair of Charney Audio Companion Voxativ AF 2.6  in my 11x15x8 room. They will play very well in the 11x13 room your considering. Charney offers 3 different looks for the Companion and many different drivers to suit your taste, budget, and gear. Don't let the small size fool you these are serious speakers that deliver it all especially deep clean multi note bass. Do a search there are a few very positive comments from owners and show attendees around the web.

http://charneyaudio.com/

The earlier mentioned Klipsch Heresy + dual JL Audio Fathom F112S sounds like a dynamite combo for a smaller room. I would venture into a different scenario with a pair of OMA Monitor’s and augment them with a pair of DIY limike’s PicoWrecker tapped horn subs. While those tapped horns aren’t small they’re rather slim (though tall), and should be placed in the corners flanking the Monitor’s. The PW's should hold their own against most any commercial subwoofer offering, but tapped horns just sound different (i.e.: better) to my ears compared to direct radiators. 

https://www.avsforum.com/forum/155-diy-speakers-subs/1654961-lilmike-s-picowrecker.html

Forget about notions of "overkill" here; it’s an approximation to sufficient headroom, and well-integrated this setup would be a seriously musical, versatile and dynamically uninhibited. 

Alternatively, and somewhat cheaper, I'd recommend the JBL 4429 as mains, still in tandem with a pair of PicoWreckers.  

I would also recommend the Aerial 5t’s. Best small speakers I’ve heard.

Because you are talking about such options as stacked Quads, I take it you are not limiting your selection to tiny speakers for the tiny room.  One of the better stacked quad setup I heard, that comes with an active crossover and dedicated EL34 amps for biamplification, is assembled by a firm named Emia.  The system is big, and can play at shockingly high volume level, and I liked what I heard in a tiny hotel room at a show.  It is not a Quad with more volume capability, so, you do have to hear it even if you generally like the sound of Quads.

The recommendation of Charney speakers is dead on.  They are amazing sounding, and work with the very low-powered tube amps which are the type of amplification I prefer (they are over 100 db/w efficient).  The model I particularly liked had the AER driver and cost something like $18k.  It is a plus that their systems are relatively compact.

You could also be a candidate for custom-made speakers.  Look up Deja Vu West (San Diego).  It is a store affiliated with Deja Vu Audio (Northern Virginia) that builds its own speakers out of vintage and new drivers.  Most of their systems are particularly suited for smaller rooms and can be tailored to match your circumstances.  The price range for custom systems is very broad, but most are in the $30k to $80k range.