Hi XXXXXXXXX this is lostrider, the reason the dealer wanted to change the differential fluid is because there is a friction modifier that they would have put back in with the new fluid, the binding sensation, noise that you are hearing and feeling is due to the rear differential clutch packs binding, the rear differential is a limited slip and uses clutch packs to perform this function, on the all wheel drives it may appear to be coming from the front end, but its actually the rear end causing the concern, I have only had 1 fluid change fix the concern, but to properly fix the truck, the clutch packs will need to be replace, there are special tools required to do the repairs, here is the service bulletin on the concern, hope this helps.
Some 2003-2004 Expedition, 2003 Navigator, 2004 F-150 vehicles equipped with a 9.75" or 8.8" limited slip rear axle, and 2002-2004 Explorer 4dr, Mountaineer, and Mustang vehicles equipped with 8.8" limited slip rear axle, may exhibit a chatter, shudder, a binding sensation, or a vibration during low speed turns. On 4X4 vehicles, the sensation may appear to be originating from the front axle or the steering gear.
. On all vehicles, turn the wheel fully right (or fully left) and then accelerate the vehicle. If the condition is verified to be in the rear axle, replace the limited slip clutch pack.
Order and install the appropriate clutch pack, follow the instructions detailed in the Workshop Manual.
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Ford Senior Master Technician
21 years on Fords,Lin,Merc