roscoe is right, it seems that most "over gear" for the given space (sometimes to the point of being completely ridiculous).
Don't like the width being (apparently) exactly 2 times the height (depends on the vaulting) due to echo reinforcement. You could narrow the room for 2-channel use by building interior false walls, but recommend reading Floyd Toole's "Sound Reproduction" to get an background on ideal room shapes (the room seems better suited for AV). Another consideration is acoustic isolation (both from outside and inside). Is this a new build or a "new to you" house? With a vaulted ceiling I assume it is a 2nd floor or more likely by it's size above a garage in which case acoustic isolation concerns would be minimal.
If above a garage how is it heated/cooled and is it finished off/insulated? Long duct runs can be very inefficient (or if not noisy). Where is the house located? A mini-split system could be an ideal solution. If a 2nd floor, recommend loose insulation in an extra set of floor joists (called sleepers) since you seem to have plenty of headroom. The sleepers can rest on neoprene pads, so as not to transmit sound down. And if 2nd floor, also suggest an insulated fiberglass door with weather seal at the room entrance.