I've had to do things like this before for customers. One solution was to build some shelving that fit in the corner like a cabinet (45 degree sides). Then the back of the cabinet was cloth (GOM) and the shelves were only about 3-4" deep for curios, nick-nacks, etc. Behind the cloth was solid absorbtion (cut into triangles and stacked up.
The cabinet was made to be about 30" wide at the front to support a full 2' wide triangle in the rear for good surface area. One customer used 703 behind the cloth - the other used acoustical cotton.
They both did a very nice job and looked great as they can be made with whatever detailing for room style you want and painted/stained as you prefer to match trim, furniture, etc. The GOM offers 48 colors to choose from so that's a nice option also.
Bryan