I would not worry with a limited-slip rear differential (this being my honest opinion)
4-wheel electronic traction control comes standard (bundled with the AdvanceTrac electronic mitigation suite) on all 4-wheel-drive equipped Expeditions. It gives the same performance as a limited-slip rear differential with none of the shortcomings. Also with it being a true 4-wheel system, it also gives the performance of a limited-slip front differential.
How 4-wheel electronic traction control is better than a LSD ...
1: It reduces drivetrain stress.
2: Driver control is not affected.
3: Less complexity means improved durability.
4: It can react faster than a mechanical limited-slip differential.
5: It will never lose its effectiveness over the life of the vehicle.
Some limited-slip differentials will lose their ability to transfer torque
as the internal slip inhibiting device (usually a clutch system) becomes
worn from use. Eventually they will revert back to a open differential, and
must be repaired.
If you want to improve traction, then a electronic locking rear differential would be a better choice. It would also complement the electronic locking center differential that comes standard with ControlTrac 4-wheel-drive.
With both rear wheels locked together, AdvanceTrac would not engage as there wouldn’t be any slipping between them. AdvanceTrac would continue to look after the front wheels and step in if either one lost traction.
Ford already has this setup in the 2009 Ford F-150 FX4. AdvanceTrac looks after all four wheels and steps in if any of them lose traction. If more traction assist is needed, the rear differential can be locked. Then AdvanceTrac just takes care of the front wheels, since the rear locker takes care of the rear wheels.