"do it yourself" acoustics

Wall-to-wall carpeting and sofa-cusion foam to dampen first reflections off of the wall. This is about all I need but I've been meaning to hang a quilt on back wall.
Also, if you're using a leather easy chair, put a towel on the head rest to soak up reflections.
BTW, the sofa foam is about six feet in length and runs about $80 (purchased at fabrics store).

13 by 13 is tough since the same frequencies are reinforced and cancelled by two of your three dimensions. If you can move the system to a different room, you'll definately be better off. If you have 8 foot ceilings, you will get artificially strong bass at 44, 87, 130, 174, 217, and 261 Hz with big gaps inbetween. Bass below 44 Hz will be hard to come by. That's tough to correct. You may need to either get a very narrow bandwidth equalizer or go to the Rives website and look into that equipment.

Full bookshelves on side walls - both, to get rid of the squareness or your room?

Agree with Ozfly that active room correction is the way to go. Suggest you also look at TacT's room correction units.
FYI, they recently lowered their pricing via direct sales.

That speaker and your dimensions are the poster child for our PARC. I don't normally post something that strong about our products--but in this case it's just the truth. Ozfly already mentioned it. In the other areas--absorption and diffusion, be sure to check out our resource section--there's lots of free advice and articles there that may help you.

Rives Audio