What a weird problem you have! From your complete description it almost sounds like the caliper bodies themselves are distorting from the pressure. You're definitely going to have to jack up the car and pull a wheel, then sit down by the caliper and inspect it as an assistant induces the noise with the brake pedal.
2006 McLareghini Bugatterrari, Storm Titanium... installed: air horn, Scroth 4-point ASM harnesses, Sector111 halon extinguisher and mounting bracket, Von Hep exhaust and rear panel delete, Pagid brake pads, red Volks CE28n wheels, Toyo RA-1 tires, Nitron SA coilovers, Sector111 (WorksBell) quick-disconnect steering wheel kit. awaiting installation: Scroth "pull-up" lap belts, Sector111 RTD Brace, Tony's heater bypass mod, and dropped steering rack mounting plates.