Good luck! I have the exact same problem that you do. I 've tried all the same things that you have, and some more: Eliminated all play in the brake bosses. Different cantis (Avid 4s to new Shimanos). Brake Booster. New fork; Winwood Carbon (It helped, but the cat came back). New wheels.
The best I've managed is squeal elimination... Chatter remains
I believe the fork is having trouble coping with the power of the brakes, and is flexing, then reflects back, to cause the chatter. Perhaps dialing just the right amount of power, through pads and toeing, is key. Correct me if I'm wrong, please.