In an act of almost incomprehensible foolishness, I managed to violate the prime edict of MacFarlane: "Thou shalt not pull the cables too far out lest ye be smited with a plague of tiny little parts."
Six tiny little roller bearings, as it turns out.
Fortunately, you won't be the first to do it, and nor was I. An extremely helpful guy named Ben quickly replied to my desperate, plaintive plea for help (it was email, so tears would have been useless) to assure me that the repair is quite simple. He also shared with me that he had done exactly the same thing on his first day working there.
It is apparently so common that they created a how-to video and put it on YouTube a couple of weeks ago: