How well does your local mechanic know Ford's? The rear differential is two parts. The gear section and the ATC (Active Torque Coupler). I'm not saying this is your problem, which is why you should get a 2nd opinion. It may just be the ATC. My wife was driving one day and the right front CV shaft splines stripped out. She paniced and kept driving to a safe spot as the AWD kept the car surging and bucking since the front axles had no traction. After having it repaired under warranty, every time I would back up, I would get a loud random bang so bad, I had to pull over to make sure I didn't just hit another car. Eventually it subsided and went away (doesn't mean it's still not broken or damaged). Replacing the rear diff with a junk yard unit (which may or may not come with the ATC still attached) would just be throwing money at the problem to see what sticks. Again, get a 2nd opinion.
FYI, the PTU is attached to the transmission and wouldn't be the problem.
FYI, the PTU is attached to the transmission and wouldn't be the problem.