Your 13 X 13 room is by far the biggest issue. you will have strong resonant modes (eigentones) in both L-R and F-R at about 87 Hz and multiples: 43.5, 174, 261, 348 Hz, etc. The speed of sound is 1128 ft/sec (sea level) divided by 13 ft = ~87 Hz. if you have a 9 ft ceiling there will be eigentones at 125 Hz, and 141 Hz for 8 ft ceilings.
Acoustical diffusers and absorbers are the only method of dealing with these. An equalizer or DSP like DIRAC can only change the speakers input into the room. They have no impact whatsoever on the output of the room from acoustic resonances. If you are in the lest interested in sound quality you must deal with those before you make any other changes. Not just my opinion, its the physics..