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It sounds like you are on the right track and have exhausted most of the options of things to check/replace. Have you seen this TSB? It is for more of a noise than a jerking or binding, but its somewhere to start. I'll keep researching more, but wanted to eliminate the simple stuff first.
It could be an ABS concern- follow these procedures to eliminate the ABS module as a possibility.
1. Disconnect the ABS module and recheck for the presence of the condition to determine if the symptom is the result of an ABS condition or not.2. If the condition goes away with the module disconnected, access the sensor cluster and inspect the connections and wiring of it. Also verify that the sensor cluster is securely attached to the vehicle and there is no corrosion of the hold-down bolts.3. If the condition is still present with the ABS module disconnected, check the rear driveshaft slip yoke for dry splines and lubricate them as needed. Then recheck operation. Always use Ford PTFE lubricant on the splines.
The splines I referred to would be on the front end of the rear shaft, not all models have splines that can be lubricated.
I would definitely say you have narrowed it down to the rear axle. If the shaft isn't connected the rear clutches can slip freely and won't bind. Have you added a friction modifier to the rear end to see if it improves?
Something must be worn out in the rear. Hard to say what exactly without looking at it. Most likely the clutches. Sometimes we will take them out and drive slow figure eights and it will free them up. That's after adding a motorcraft limited slip additive.
I'm sorry, I attempted to respond a few weeks ago and it looked as though the question had been closed. It seems it has been opened up again. Let me do some research and see if Ford has any insights for us.
Have you measured the circumference of each of your tires? According to a bulletin from ford the circumference of each tire can be no more than .5 inches different from one tire to the other. They suggest using a string or flexible measuring tape to check the circumference of each of the tires.
You might also try disconnecting all wiring that leads to the transfer case and then road testing to see if the condition improves or worsens.
That cuts off the sensors in the front axle too. You will probably want to try it at the T-case to eliminate it separately.
Do you have a scan tool to check speed sensor readings? You might a have a speed sensor problem.