Credited to Frank Montesinos:
"Figured I'd post this in case it helps someone else. If you've had what sounds like a buzzy/blown center speaker on the dash, it might just be the grille vibrating. It was really bad with loud phone calls. I just pulled the grill/vent trim piece and added small, thin felt pads. I first just did it mostly around the speaker, but still had some minor buzzing, so I went back and added more.
For reference, this is a 2013 A6 3.0T with the Bose system."