Overlooked room treatment for too long - what do I do?

My wife, who used to work at Magnolia hi-fi years ago, turned me on to the concept of how the different surfaces can affect things.
One day when we were moving a cedar chest into a room I use for listening, she quickly grabbed a small bathroom rug that fit the top of the cabinet perfectly, and put it on before I could get the gear back on it.
I didn’t question it, and was quite pleased with the result…

I have since followed up with basically a quilt hung onto one wall, that also helped a bit. Tends to be optimal overall to not have two reflective (hard) surfaces opposite from one another.
 
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A used heavy theatrical curtain can be used in place of a wool rug. Can be quite effective. Also, just as a quick check a packing/shipping blanket (used for putting between items shipped long-distance on a truck), can be hung on the back wall. Let the bottom touch the floor and pull it out a little to leave a little space behind it.

Also, the guitar hung on a wall is going to be a resonator. You might try with and without it being there to see if you can hear any difference.
 
My experience of damping the back wall if you sit close to it, is that too much damping is not preferable. That is because you change the tonal balance too much. You could apply damping but for the higher frequencies only, say above 1-2khz, where path length differences between the direct sound and the bounce against the back wall become noticable. So you avoid the so "called flutter" echo but also avoid a duller sound.
 
Flutter echo is yet another phenomenon. The issue with your head near walls with absorption is that even with high values of it the reflected wave still is noticeable and ruins spatial information.

If the tonal balance is changing, the absorber isn’t doing what it has to do. Which is pretty normal. If you ever took a listening session in an anechoic room, you know, the one with the 3ft wedges and your head near the tips of those wedges, you could have learned that a good absorber does do the trick perfectly.
 
If you ever took a listening session in an anechoic room, you know, the one with the 3ft wedges and your head near the tips of those wedges, you could have learned that a good absorber does do the trick perfectly.
In this exemple, there is no reflection at any frequency, so fairly logical that it does the trick. In the real world, absorption is frequency dependent and in my experience too much damping from say 400-500 Hz (5cm of acoustic foam) is not the solution. So a thinner wall carpet may work better. I tried this at a friend with the same problem -sitting too close (1.5 ft) to the back wall in a small living room. Against expectations, it sounded better with no damping material on the back wall -although in the beginning you think with damping is better, until you remove it.

The time difference between the back wall bounce and direct sound is well within 10milliseconds, so it may not be perceived as two different sounds and blend together. The bigger problem is lower frequencies building up along the wall that changes tonal balance and those frequencies are not easy to absorb. For higher frequencies, instead of damping the back wall behind your head, damping first reflections between the speaker on the front wall and the first reflection points on the side walls could be more effective. The only way to know is to experiment.