My room has three large windows on the left wall with plantation style shutters. The speakers are designed for a 45 degree toe in but I prefer them at 40 degrees. Therefore, sidewall reflections are not a major factor. The toe angle intersects in front of my listening position. The speakers also have a side firing tweeter which on the left side is 23 inches from the window so there is some direct sound involved from this.
I prefer the sound with shutters on the first two windows closest to the speaker pointing downwards and the third window shutter pointing upwards. In this configuration the imaging is more precise and the bass better defined. The right side speaker intersects on axis with the third window. With the shutters open to the horizontal position, the sound does get brighter and less focused. Fully closed in this orientation gives a more intimate denser sound.
Reversing the orientation described above results in larger sound with bass that is less defined and a more forward presentation.
I'm satisfied with the sound and the opportunity to make adjustments with predictable results. In my environment of AZ, I need to block out the morning sun as much as possible. Buy the shutters. I think you will be satisfied.