Well, I did a lot of city driving today and had plenty of chances to investigate the sound. I was wrong, it does show up when engine braking. It mostly happens on a shallow left turn but I did have it happen on a straight, level section of road, and I think I even heard it at a low speed right hand turn (pulling out of a parallel parking spot). I heard it happen at up to 20 mph. It could be happening above that and is being drowned out by road noise.

Also, it was raining on and off all day, so weather doesn't seem to be a factor.

Any pressure on the brake pedal instantly stops the noise.

I don't expect this'll bring about any new ideas, just figured I'd document it. If it is the brakes (and I'm leaning in that direction based on some of the above posts) maybe I'll use this as an excuse for an upgrade