I took the brakes apart last night to make sure they are good and they all look fine. Plenty of pad life and everything is wearing evenly.
The issue is the dust guards on the rears were disintegrating into bits of rusty metal that were falling into things and making a racket.
Here is what one looked like after assaulting it with a screwdriver and some side cutters. That should solve it.
Not pictured: my refreshed drop light putting in work.