Hi thank you for your question I can help.
You are right there is a TSP out for this problem. But it is a TSB not a recall so if you do not have a warranty you will have to pay.
I would not recommend letting the dealer do this work. Any reputable shop can do this repair, For a lot less money.
Yes rebuilding or replacing the rear end will fix the problem for good.
The problem is ford used cheap bearings at the factory that are wearing out to fast.
The TSP calls for rebuilding the rear end with new parts Listed.
THE AXLE SERVICE KITS INCLUDE THE FOLLOWING COMPONENTS:
4630 - Head Bearing
4628 - Head Bearing Cup
4676 - Pinion Seal
386989-S2 - Washer (Slinger)
4621 - Tail Bearing
4616 - Tail Bearing Cup
4222 - Differential Bearing Cups
4221 - Differential Bearings
4209 - Gear Set (includes pinion shims, pinion nut and crush spacer)
4209 - Instruction Sheet
The old TSB 05 -12-6 for this problem called for replacing the rear axle as a hole.
Now they just replace the bearings and seals. (Rebuild the rear end).
This is a copy of the TSB click here
The rebuild kit online or from a 4x4 shop will run about $300 total.
The labot to do the job should not be more than $600
Let me know.