So I'm back from yet another visit to my dealer. I got the same technician, and this time around he got another technician to ride along. They both heard the sound again, but I think the conclusion was "we're not exactly sure what it is, but we don't think it's a problem." I'm not sure if that's an answer that I'm comfortable with. I've read some other threads here with similar noises coming from defective clutches or differentials, so this is still freaking me out (FYI, I tried the old WRX trick of changing front/back tire pressures with no effect).
Before they gave the car back to me, they said that they adjusted the heat shields (based on what I see, this means they bent the edges a bit to make sure they're extra tight). Maybe I'm hallucinating, but I think the sound is louder now! Unfortunately, it's raining right now so it's hard to tell for sure. But if it really is louder (which I'm kind of hoping for), that would be conclusive evidence that it's a heat shield issue (because they didn't adjust anything else).
I made a new appointment for Monday morning. I'm hoping that it'll be the last! I think this time around, I'm going to ask them to just pull all the heat shields and take a drive to determine if they are actually the cause of the sound (maybe I should have asked for this already).
Also, I made a better recording of the sound: http://www.squicky.org/tmp/subaru/scrapey.mp3
Anyway, if anyone has any additional thoughts, they'd be much appreciated (even if it's just another "sheesh, it's a normal Subaru noise, deal with it"