I'm don't think Ford offered body wraps on the 21's, looks like a shop did a crap job. Ford just started to offer factory wraps this year I think.
I'm guessing you bought it used?
Yeah, I hate those butt pucker moments, glad you are Ok!
I change my tires every 5 years, don't really drive as much anymore. But the Falken Wildpeak AT/4Ws are on my list. Love the falken's that came with my Badlands, no complaint's.
Wow, sounds like you've check about everything. Might have to get someone to ride along and see it they can pin point the source.
Just for grin's, check the roof rails and antenna. Make sure the rear seats are latch in position.
Can't thing of anything else, best of luck...
Check this seat belt adjustment. I had this rattling when I first got my Badlands, found the adjuster was between positions (Full up or down) and was driving me nuts. I put the adjuster in full up and it solved the rattle.
Full Up
Full down