Just for starters, a thick rug and curtains for the sliding glass door will take a bite out your problems. Wall hangings, bookshelves and other furniture will break up sound waves as would large plants. Sometimes dispersion is preferable to absorption. Over damping can take the life out of the music. Bass resonance may be your biggest obstacle, but if brightness is the problem you may be able to tame the room without professional assistance or electronic correction.
