I think I (finally) figured out my issue tonight. I could tell the noise was metal on metal, but I always assumed it was coming from the parcel shelf itself. Turns out, it was coming from one of the points where the parcel shelf attaches to the frame of the car. The below photo was taken from the passenger side, just behind the back seat. You have to pull the carpet back a bit to get to it.
When pulling the parcel shelf side to side, I was able to reproduce the noise. After trying several spots, I pried apart the metal in the spot circled below. Success! I also sprayed some white lithium grease for good measure.
My issue could very well be isolated to my BRZ, but I figured I would post it just in case anyone else had a mysterious noise coming from the trunk area they were unable to isolate.