I would definitely install wall-to-wall carpeting with a nice thick pad underneath. I'd put thick wedges on the angled part of the ceiling, possibly some on the rest of the ceiling too. It would probably also be good to put some wedges on the walls beside and behind the speakers. The opposing walls could be left more open, possibly that where you could put artwork and shelves. Might do a few tiles of wedges and experiment, find what sounds best.You don't necessarily have to entirely cover a boundary surface, although the floor and angled part of the ceiling probably should be. The other surfaces may have partial covering. If you toe-in your speakers like I do, I'd want the adjacent sides absorbent, which would be beside and behind the speakers. That just helps reduce early reflections, something the directional nature of the speakers already does but the absorbent room treatments go further in the right direction. The reflection from opposing walls tends to give an impression of spaciousness so I wouldn't want those walls to be overly deadened. Experiment to find what sounds best.
Would you be opposed to using this stuff?