Update #4: Well, bad news. There's currently no fix for this noise. The dealership called me and said the field engineer is aware of this issue in other BRZ's and FRS's and that there is a TSB for it. I don't know what the number is, but maybe they'll tell me when I pick up my car later. Since there's a TSB, it should get fixed eventually, but it could be months or I guess even years. As long as it's documented in their system, even if the car is out of warranty, they'll have to fix it once the fix is available (dealership told me this).
If/when they give me a call for a fix, I'll update here.