I just got a response from the host (Media Temple), and they tell me everything is fine again, though they didn't do anything. They attribute the problem to "bad neighbors" on the server, and promise to find and nag them into oblivion if this happens again. In other words, they don't know what's happening any more than I do. But, the site does seem to be working again, so dive in and have fun. Please let me know the second you see any more of those error messages so I can hassle MT again. Thanks, guys...
Max