I almost forgot about something that has happened to me.
On my '99 C4 I got what sounded like the brake lining had fallen off the pad and I had metal on metal contact. It's happened more than once.
Turns out that the gravel DOT uses instead of sand is just the right size to bounce up between the rotors and the weather guard on the backside of the rotor. Once it's in there the guard acts like a sounding board.
Not quite the sound you describe but try stopping and rolling slowly backward. Maybe you'll get lucky and have a passenger that can get out and listen for where the noise is from.
Once I had to take the wheel off and use a piece of Alum TIG rod for a probe to wiggle it out.
First time this happened was before I replaced the O-rings in the spark plug tubes.
Went screaming down the on-ramp and as looked in the mirror I saw smoke and a gawd-awful screech from the back of the car.
The noise didn't stop until I hit the next off ramp and found safe spot to check out the heck was going on. Rolling backwards cleared that one.