I'm guessing a bit here because I can't take the data acquision system and strain gauges I use here at work out the road. The power cord is too short, I can't find anybody who can run fast enough to push it, and I'm afraid of getting rear ended when I apply the brakes while towing it.

First off, this is the only time I've ever had a brake squeal problem I couldn't fix with a basic toe-in adjustment. Black Kool Stops were the first thing I tried and they made the problem a little worse. I toed them in a bit more and it helped but it wasn't a solution so I put the old Shimano pads back on and started looking elsewhere. Too much toe-in is only a temporary fix anyway. As soon as the nose of your pads wears down enough, the squeal will come back.

I think the natural frequency of the fork cable interaction was close enough to the brake boss lever shoe interaction that the oscillations were driving each other. Having the fork crown clamped really hard in the headset and lengthening the link wire damped and lowered the first resonant frequency. At that point, the black pads moved the two frequencies closer together and the salmon pads moved them further apart. It's a cross bike that sees a lot of commuting and limited touring duty anyway so severe conditions pads aren't a bad idea.

Given no alternative to consider, this is the only explanation I've come up with that makes sense to me. I suspect serious brake squeal issues often have more than one cause. It's easy go after the primary one, the brake shoes and their position, and ignore the others because it usually works. You increase the damping and/or shift the natural frequency of the first cause and there is nothing left driving the second cause hard enough and at the right frequency.