Had the same problem with a 08 F 350 long bed diesel. Ford has a twix out saying that the driveline angle is changed when a heavy load is pulled. They shimmed my rear axel so there is limited shimmy under heavy load. You have to remember that if you shim too much it will vibrate and if you shim to little it will vibrate. A split drive shaft will solve the problem but that adds cost to a new truck.
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