2006 GMC Sierra terrible vibration

I have a 2006 GMC 4X4 with factory 20 inch rims. It has a terrible vibration/shake, when the brakes are applied. Doesn't appear to be related to warped rotors as they were turned once and later replaced, with no improvement or change either time. Shake is inconsistent, sometimes it nearly shakes the steering wheel out of your hand, other times it is not noticeable or nearly non-existent. Always present when attempting to slow while coasting down a hill. Have rotated tires with no change and also replaced a bad wheel bearing on the front driver side, also with no change to vibration. Sometimes you can rapidly pump brakes and stop the wobble, other times this has no affect, however when the brakes are released the shake always stops.