I'm actually dealing with something similar but its not audible. ( I posted about this on the Ford Raptor Owner's Group on FB )
For me I'm getting the vibration from the ass end that feels like the first inch of bump travel isn't being dampened by the shocks. If you think of a sign wave, I'd say its about 4-5 waves before it settles out after the bump. I'm the original owner and I can positively state that the truck has not done this for its entire life.
As of now the truck (2013 SCab) has 52K miles on it. The factory shocks were replaced roughly 1000 miles ago all the way around and that changed nothing. I just replaced the leaf springs with the ICON springs 100 miles or so ago and that too has not changed the feeling. When I did the springs everything was torqued to spec with while the truck was under its own weight. I reused the factory shackles and checked to ensure they were in good order before reinstallation.
Spare tire is tight up to the frame, and the left frame rail weight is in tact. In the past I've ziptied the weight into a fixed position and this had no effect. I'll give that a shot again I guess to be sure.
Yesterday I did a few dump runs with roughly 150lbs or more of brush/tree material in the bed and that DID help a fair amount I will say.
- Travis