@panzrwagn has it right.
The acoustics treatment route is the only way out. If it were my space, heavy theater curtain type drapes (so you can completely close all the glass off) would be step one. That will cost a more than the speakers probably. Then progressively more treatment on the floor (rugs) ceiling (cloud/panels), until the reflections are tamed down enough to get a decent balance. After all that, if it still isn't great then correction software like Trinnov (that works on good rooms and speakers to amp them better) would be worth trying out.
"Room correction" is a complete misnomer as you cannot correct physical acoustical problems without changing the physical properties of the space. Electronics cannot fix room issues, it can make them less apparent in one or two locations but it will never "correct"/ "fix" them. We work with Trinnov on the pro side and there this type of software is called room optimization-which works on the way the speaker sound and the room sound combine with each other and create a third sound, the sound you hear.
Brad