If it's what I think it may be, there's a test that might determine it. However, you'll have to shoot the gun with the brake on and off. If it was to be barrel resonance, adding a weight of some sort off the bottom of the barrel, toward the muzzle, will tend to cancel it. If it does cancel it, then there might be a chance to just set the brake about 1/4" to 1/2" back from where it is now, of course you'll lose a little in barrel length to do it.
Sometimes, its a combination of things, from the barrel length, rifling twist, type of steel, and the load, that can cause this, and changing one can nullify it. Adding a clamp-on test weight just lets you know you're looking in the right direction. There are adjustable muzzle dampeners for this too, that attach on the end of a barrel like a brake, but don't do the same thing.
A good way to explain resonance, is an automobile on an interstate, that has the sleep-bumps on the berm of the road. If you hit there, with your tire, at the right speed, and then pull off them, the resonance thats set up in the spring will cause the wheel to keep on hoping for a bit. Another example is like when a wheel weight falls off, and the tire will vibrate at a certain speed. Its funny that barrels can do this too, for some reason.
I don't think the action is shifting in the bedding causing this, as once it shifted, you would have a problem all the time. I take it you keep the torque off the action when removing the brake? If so, and you hold the barrel, as you unscrew the brake, then I think it has something to do with stressing the barrel, and its sensitive to about anything done to it in the way its made, especially when its fired.