This, of course, was the correct advice, which explains why I didn't listen to it.
Getting the stripped screw out was very difficult and I ended up nicking the metal portion of one of the earcups. Nothing terrible; a couple of small, visible nicks. But stomach-turning for the likes of us, and I am upset with myself for doing it. I'm no DIY expert, but I do know that these Stax screws with the headphone assembly suck ass. Now I need a new one to replace the stripped one, and I'm not sure where I'm going to get it. Maybe Ratshack. Hardware stores around me tend not to have such miniature screws.
Luckily, I do not intend to sell these anytime soon, as I have come to love them.