JE, my guess is the moderator is the expert, but in lieu of that, I also have an open wall on one side, but not completely open so no so bad. I did experiment putting a single piece of plywood (drywall, or any 4x8 sheet) and could not tell that much, but in your case i'm guessing it would help. As I've said in other posts, my DIY Shakti Hallowgraphs (contact me for more details) work really well with adjusting room ambience. Not sure why midrange would be problem, could also be other equipment i.e. if you are thinking of changing your pc I have a lessloss cable you might be interested in, but that may be a last resort.
My thought for a wall would be to construct one that is maybe 4 feet high (4x8 sheet on edge as a temporary experiment)using standard 2x4 studs. Make it just large enough to be able to make it modular/mobile and move into place and see what you are hearing. Perhaps check cables, tubes, etc. Good luck!