The carpeting is your acoustic treatment- it makes a huge difference in reflections and the OP has an area rug, vaulted ceiling and much more surface area where the sound can reflect. Your low ceiling makes the path length for the reflected sound to be closer to that of the direct sound, so any difference will be less audible- if the OP's room, the reflected sound from the ceiling is late enough that it WILL be apparent and problematic.
The left wall will have a small effect because of the window frame nearest to the left speaker, but the table and everything else on that side will do much more, causing an imbalance in the sound. Drapery or shades will help, but it would be best to find something that isn't too absorptive because the right side diffuses the sound, it's not being completely absorbed.
Speaker dispersion makes a big difference in whether a given room will have/be acoustically good or bad- more direct sound and limited dispersion in a live room is better than extremely wide dispersion.
I used REW in my room with several speakers, including the most recent- you provided the crossover design for those. All had phase cancellations in the same area and it made listening and being satisfied with the sound mutually exclusive- if I moved to either side more than a small distance, I could hear the effect and I have learned to be very sensitive to phase issues over the years. The old REW results are in an old laptop- I'll see if I can find them but the image is from the Dynaudio RTA app, which I have compared to REW, used at the same time and it was similar enough that I would say it's pretty accurate. This was with pink noise, at my listening position, not at 1 meter and without any kind of subwoofer and the peaks were from normal amplitude changes when using pink noise.
I had some panels left over from a project when I was working with a friend on a home theater that had serious problems with cancelations in the low end, which wouldn't have occurred
if the insulation had been installed between the studs in the wall at the right. When the panels didn't solve the problems, I thumped the wall, out of frustration and it sounded like an undamped drum head. We opened the wall on the backside and saw absolutely no insulation- ironic that the homeowner has an insulation company and all of the construction was done by his employees. Once the wall had been insulated, the problem was gone.
When I decided to deal with my own room's problems, I brought the panels inside and left them in a place where they wouldn't affect the sound until I placed them at the first reflection areas at the side and behind the left speaker, watching the response change as I moved them. As I added panels, I could see that they WERE helping and eventually, the dip in the response was gone.
It's a fairly small room, irregularly shaped and the speakers are asymmetrically located. I spent a good amount of time finding the best location for them to prevent major differences in the midrange and highs. The left speaker is a few feet from the left wall, the right is about 6' from the right wall and the wall at the right stops about 6' from the back wall before opening into the kitchen. At the right rear is the doorway to the rest of the house, so that corner needed no correction. I added panels in the rear corners and behind the speakers- I can now move from my main seating position to others without hearing terrible sound.
Acoustics is a mature science- if you don't think acoustics is considered in the design of all concert halls, old or new, you're mistaken. They aren't designed to be used when empty, but large vs small audiences is part of the consideration and if you have seen panels near the ceiling of a hall, those are usually called 'clouds' and are often movable
shop velvet sofas, to provide the desired response at as many locations as possible.
