Hi;
I'm an industry guy who's had the privilege of serving as the lead designer & project co-ordinator for quite a few private theaters / listening rooms. I like music, so almost every room I've ever been involved with on works for 2-channel listening as well as with movies (you might be shocked to know how many "professionally done" home theaters can't produce a decent 2-channel stereo image). While we all have our biases based on personal preference and different experiences, I absolutely agree with James that over-damping can be a negative. As he's said, this is largely because real-world damping is typically very efficient at high frequencies, with effective absorption declining as frequency falls. So it's easy to wind up killing high frequencies disproportionately with mids. Subjectively, and in my opinion, peaks in the upper mids do more to make a system sound artificially bright and harsh-sounding than some moderate lift in the extended highs. (This is why almost every element in the signal chain for electric guitars is almost always designed to "peak" the upper mids - so that the guitar sound can "cut through" the other midrange voices & instruments on stage or in a mix.)
When we design theaters, even with all wall surfaces covered with fabric for a harmonious appearance, there are different materials behind the fabric, according to location. These would typically include absorption, reflection, diffusion or diffraction. Absorption and reflection are the most important ones.
Most of us, who love music and the gear that makes it sound good, start with existing rooms that need some modification to be better for listening. We don't usually have the option of a large undeveloped space that can be designed from scratch, with sufficient size and volume to permit extra-depth walls or room-within-room construction to improve wide-band frequency response within the shell. So what works best is to nullify the worst of the problems, and in the process, not to create new ones (over-damping of highs can result in both dull AND boomy - not good).
Some damping of high frequencies and down through the upper mids almost always improves how you perceive imaging. Generally speaking, if you want to tighten up and make that aural perception of an instrument or vocalist at a specific point in space more believable, you have to reduce the destructive effects of the early reflections, slap echo, etc. from nearby surfaces. The closer the room boundaries, the greater the benefit of some absorption.
To the OP, from your pics, you already benefit a little bit from the drop ceiling and ceiling panels (not much, but if you feel you want to experiment, you can buy panel replacements that are rated for sound absorption). It also looks like you're listening across the short dimension of the room? This has the benefit of leaving lots of space from the speakers to the side walls, so that the reflections have a longer propagation time back to the listener compared to the main sound; if this time is long enough, the reflections detract less from the primary sound.
I appreciate that there are always conflicts with appearance preferences, but if you were to consider a much larger area rug, or even wall to wall carpet, that would also help.
An easy way to find the most destructive locations of early reflections is just to sit in your usual listening position and have someone move a mirror along the side walls so that you can see the mirror. The spots where you can see the speakers in the mirror are the first locations to treat.
Is the sofa against the rear wall? Or is there some distance between the primary listening position and the rear wall? Unless there is a substantial distance, you might also consider something on the rear wall, behind your listening seat. You have a number of options for this, from purpose-built panel(s) to a decorative rug hung as a tapestry.
I'm with James when it comes to bass traps, they're not always what they're cracked up to be. The main problem is that they can result in an unbalanced end result - you absorb in specific physical locations in the room, corners for example, but you're absorbing so selectively that the net improvement may not be what you hoped for.
But I'm definitely in the camp of favoring some absorption, and it can be one of the cheapest and most effective improvements you can make to your listening experience. Just don't overdo it.
Hope this helps.
Brian
