Room is way too bright.

Elimination of reflections of hard side windows has been discussed. Don't mess with the content or origin, simply eliminate the problem temporarily when listening, that's the flexibility of Acoustic Fabric Vertical Blinds. Keep all that daylight, a few live plants, a living space, not a dungeon.

Toe-In combined with Tilt, directing the tweeter's output in and up to your seated ear height, will give preference to direct, essentially equal volume of primary drivers, minimizing reflections from floor, ceiling, and side walls.

Ability to adjust frequency balance at listening position to your preference is important. CD with test tones to document pre and post adjustments, 

Amazing Bytes, CD with 29 1/3 octave test tracks

and SPL mic on tripod

SPL Meter, with bottom hole for tripod mount

are needed, then use your ears, a helpful friend is always good.

Open Space behind you increases the time delay of eventual reflections. Diverse mix of angles reduces similarity of reflections to initial direct sounds.

Adjustable Toe-In for Imaging, for Single Centered or Two Off-Center Listeners

Toe-In Alternates, Stereo and Video

Having a picture of your space may help us determine solutions.  The ceiling panel, also known as a cloud, is probably your best bet without covering your windows with absorption.  Handling that ceiling bounce will at least mitigate that reflection angle and may make the space much better.  I also agree with speaker placement and toe in are critical and by moving your speakers away from the windows, you can reduce the amount of acoustic energy hitting the walls.  DSP and cables are the absolute last thing I would do.  Building panels is not hard, or you can reach out to a company like gik acoustics and order paneling from them. 

@8th-note

I really like your approach!

As noted by others, reflections come from the walls and also the ceiling and floor.

If you want to minimise the accoustic mess created by different length reflection paths, use speakers with a minimal number of crossovers and separated drivers.  Think point-source, or an approximation of it.

That way the reflections are at least coherent, making it much easier for your ear/brain to hear through to the music.

As Magnepans essentially don’t radiate to the sides, I’ve found them to be much more forgiving of rooms with glass on the sidewalls.

I can open my blinds all the way and the sound is still good, just a bit “lighter” in tonality.

I can vouch for that Magnepan comment. I have some Magnepan Minis in a 10 x 13 x 8 open room. I have a CD rack near the left speaker and a huge TV placed on the floor of the right speaker. If I used non-Magnepan speakers in this space it would be crazy reflective and fatiguing. The Mini sound very good in this compromised space and the only speaker that I have owned that I do not worry so much about the first reflections.