If there is cupping on the tires, you will have vibration and noise.

Mudders are noisy, period....

Before you rotate the tires, take note of the steering. If the front tires are smooth (no cupping) there should be no vibration in the front end.

Putting the cupped tires on the front should give you a slight vibration.

While you have an alignment, you have checked the front end. Now, has the rear end been checked for correct alignment??? ie, springs centered and square with the front...

After all, you did re-align the rear with the lift....

High probability it is the tires...