Drew, I know that this is not the perfect answer, but I too, have a room with the same associated problems as yours. For me, after doing all that I can with positioning, etc. the coarse/fine volume control helps somewhat. I guess it's not much different than a balance control, and I know that this is not a balance/volume issue, but it helps non the less. I agree with Graingers idea of using a mirror to locate those reflections most troublesome. There may be a point of diminishing returns given the conditions in the first place, but it's all we can do.
One last thing, I did experiment with sticking my entire system in the corner, giving all new directions for the reflections. Results were mixed but not unpleasant. My wife thought otherwise.