Haha. It turns out that not only was the alternator bad, the battery was on its way out, too. When idling, the system voltage was now a healthy 14V, but the battery was low enough the next day that it wouldn't start! Luckily, my folks also have a VW from the same era, and Dad just happened to have a newer battery that he bought when theirs had an issue. Here's hoping that the car stays fixed for at least a little while!