I rarely am sitting in the "sweet" spot and am almost always moving around.
In my living room there (where the stereo is) is a bay window (about triple the size of a normal window on the right (as you are facing the stereo), slightly longer side wall, naturally causing some side reflections. I do not have any form of DSP (yet) but have done something that is A. adjustable B. the adjustments affect the reflections form the bay window C. this was accidentally discovered through my wife's, natural design inclinations.
She had me hang a 2/3 height (from the bottom of the bay window 2/3 to the top of the bay window) standard grey (lets some light through but not shear) curtain that fits almost flush with the wall & 2 & 1/2" beyond the sides and is 1" longer than the bay window (this leaves about a 5" gap between the curtain & the bay window [she said so that I could walk around with no shirt on] {I am always warmer than she is, so, around the house, when she is dressed normally, I am in slippers, shorts & no shirt or a light T-Shirt} but could not be seen by people across the street during the day, yet some daylight could come in).
She also had me hang a full length shear curtain (just in front of and starting from 6" above the top of the bay window to the floor. This curtains folds back edges just touch the other curtains folds front edges.
In addition, she had me hang a third full length curtain that has alternating 14" normal & shear sections (both a bit thicker weight that a normal floor length curtain has) that run the width of the curtain 3" in front of that curtain.
The next time I turned the stereo on, I realized that the higher frequency reflections had been mitigated some & that I could adjust their effect by adjusting the curtains.
I hope that this information can help you with your problem in some fashion..
EJ3