I am by no means a mechanic so if this has already been done, I apologize in advance.
1) What type of roads is it being driven on?
(If possible, try to drive on both asphalt roads and concrete roads above the symptom speed)
2) Place 200-500 lbs of whatever in the bed and drive above the symptom speed.
If it's shake disappears then you have the beaming shake and GM recommends the following to correct:
Replace the body mounts:
Upper Mount (Part: 25791031) - will need 2
Lower Mount (Part: 25791032) - will need 2
Washer (Part 15854745) - will need 2
In addition, I noticed that you stated that you had the tires balanced, my question is whether you had them road force tested by a reputable shop and reviewed the printout?
Not to be a pessimist but did you actually verify (or have a shop verify) that your rotors (although new) are straight and true?
I also agree with Darral as noted above: check for any missing weights on the driveshaft and have it checked/rebalanced by a reputable shop.
If you have not already checked, see about checking the wheel hub / axle flange runout. I believe the tolerance should be .127 mm (.0050 inch)
Lastly but not least, check the wheel stud runout. Its tolerance should be .8 mm (.030 inch).
The above list is not in any particular order, I would check the run outs first (if you have the appropriate tools) since those can be done by yourself for free (who doesnt love free). Everything else will cost $ so I leave it up to you. Let us know how it turns out
