I doubt it's your ceiling. It's the open passageway and the glass door. My living/listening room is similar in description, (except with with more openings and no glass door), and the cathedral ceiling is the only thing that keeps it from being a totally hostile area for music reproduction.
The passageway is a big bass trap. The glass doors will cause bass problems in a big way. And on top of that the 15' width of the room will cause low mid-bass standing waves.
The passageway is a big bass trap. The glass doors will cause bass problems in a big way. And on top of that the 15' width of the room will cause low mid-bass standing waves.