Light / porous enough for air to flow in.
Should be available at a fabric outlet.
A pair of these
sitting somewhere approx. between the edges of the flatscreen and the inner back speakers, at an angle (experiment) (i.e. neither parallel nor perpendicular to the wall behind) will work wonders. Depending on the amount of space, you may not even have to move them to watch TV.
Front wall between the speakers one would be more inclined to use diffusion as opposed to absorption, but given your limitations, anything will be better than nothing.
A blanket as suggested is going to work over too limited a frequency range. Heavy pleated curtains may work well as the first wave from the speakers will be at a sharp angle and hit multiple pleats.
@audiozenology is correct... Any diffusion or absorption is better than nothing... I would look at putting a 2 inch thick wideband absorber over the surface of the plasma TV and some diffusion above and to the sides if there is room... I use a GIK Art panel my self with a custom image I supplied... Sure you will have to rig a custom padded bracket to hang the absorber over the TV with but it will be worth it... Use REW to "see" what is going on in your room... I would guess you might need more bass trapping also... Good luck in your quest for audio nirvana...
Ok, so I tried eric_squires' suggestion and hung a large down-filled quilt over the entire surface of the TV. I invited my audiophile, musician friend with excellent hearing over to listen. We played several pieces of classical, jazz and rock with and without the covering. After several with/without, with/without back and forth, the verdict was unanimous. Voices lost their luster and instruments lost their realism with the covering in place. Go Figure! I might try other solutions but now I'm wondering if there is really a problem!
Coincidentally, I had a sixty-five inch flat screen between and just behind the plane of my speakers. A lighting surge took out the TV several months ago. If my stereo was a four on a scale of one to ten it suddenly became a six or seven without the TV present. The replacement TV has been sitting in our foyer in the box for at least two months. The stereo is immensely better without the big reflective TV there. Even my wife can hear the huge improvement in the stereo to the extent that she hasn't pressured me to set up the new TV.
Identifying a single data point is attribution, not causality. There is no way for you to know of "contributions" from other variables. For example (being cheeky) one might say it was the lightning surge that "treated" the room or (being cheekier) your power cords. : )
You need to test and retest to be certain. And yes, that means putting the new TV back on the wall and removing it, and putting it back on. It’s wise, smart and educational to confirm or eliminate.
A "four" to "six or seven" jump (your measure) is a 50% to 75% jump in system performance.
If my stereo was a four on a scale of one to ten it suddenly became a six or seven without the TV present.
I’ve experimented for years in my room. Before putting your wife to work, go find some dacron. It’s available at upholstery vendors in various sizes. It can be halved by carefully separating/splitting it, for experimentation. In large rolls, it comes mostly as 3/4 oz or 1 & 1&1/4 oz thicknesses. I use is currently behind my thin curtain on the front wall covering my center window. I just hang it with zip ties to the curtain rod. Experimenting with different thicknesses is very enlightening.
IME, going heavy, sucked the life out of the music.