Is it even possible to set up a system in 12x12 room?

Another thing that you can try is to toe the speakers in so that they cross in front of your listening position.  Looks weird but it can work in some circumstances.

We see plenty of systems with the loudspeakers too far from the front wall. Yes, too far. For whatever reason there is a commonly held belief that 2, 3 feet or more is needed for good depth of soundstage. In practice, many loudspeakers can be ideally placed much closer to the front wall with better results in every aspect. Bass, imaging, width of soundstage, and better sound from more listening spots. 

If you would like help just let me know. I can walk you through the process over the phone.

Yes. Also try setting up your system at 45 degrees to a corner 
this eliminates a lot of the dead’s and highs with a square room and setting the sound coming from one end 

Most people never have the 'ideal' imaging triangle, their listening position, like mine and most of my audiophile friends, is further back than the width of the speakers, by a few feet or more. Usually that is combined with the rear wall being farther back than you will have. 

I have equal triangle in my office, and using small B&W bookshelf speakers with a powered sub, it is quite enjoyable. I get just a bit from the sub, you should only notice it when you turn it off.

Your room will force the near perfect triangle. It's problem is square and rear wall right behind you. You will definitely need to strongly reduce reflections off the rear wall. Less bass from the speakers helps.

Using the smaller speakers, toed in a bit away from side walls, perhaps tilted back a bit (not parallel to floor and ceiling), and only going for 40hz, no port is my suggestion. Then, tame the rear wall. Then, if you want, try a small powered sub, but don't go overboard.

Tweeters at seated ear height, bass below that.

Small size speakers and small size sub to enable alternate positioning. NO PORT!!!!!!