There are other alternatives to consider that are less expensive too. Without knowing your house layout (1 story or 2, location of room, etc) I'd venture to say the carpet and drapes present NO problem at all. The drapes probably BLOCK heatflow through the window, if it is on a southerly-exposed wall. If so, even planting a diciduous tree of the correct size by the window will help with the cooling.
Also, you could divert MORE of the AC TO your AV room and let your other(s) room warm up more, if your lifestyle would allow that. That can be accomplished by having an AC tech install dampers in the ductwork, allowing you to direct the flow to the rooms you choose.
Hope that helps or gives you some ideas.
Good Listening & L@@king!