I suggest that you sit in your sweet spot and have someone run a mirror along the wall. Wherever you see a tweeter from your fronts in the mirror, that's an area you have to treat. Do this along your ceiling too. Try temporarily placing some soft material in those areas (eg. towels) and see if you notice a difference. If so, you will then need to purchase some room treatments. One for each side wall and two for the ceiling would probably work well in that room for starters.
The geometry of your room is such that you will most likely benefit greatly from this particularly at higher volumes.
