I was having trouble with the headphones not being a clear enough signal so I took a 3'x4' black foam posterboard and made a cubicle door. It caused a stir but mostly just in the people who liked to come by and ask me if I'd opened the cat gif they'd just emailed. Having the door closed is a nice clear signal and so far it's worked fine, for exactly your reasons. I can now trust that I won't be interrupted and I can relax to focus.