Hey Rusty, it looks like Hammer beat me to it. Both the Owner's manual and shop manual are in agreement with what Hammer posted (*those numbers include 0. 05 L or 0. 25 pts. friction modifier). Fill to bottom of fill plug hole.
You can identify which axle you have by the Identification tag on one of the cover bolts or by the looks of the rear end cover. The 8-1/4" has an oval cover while the 9-1/4" has more of an octagon cover. Procedure is basically the same as that of the Ram. Perform your low speed figure-8's after adding the modifier to work the lubricant into the clutch discs on the Trac-loc differentials. Also, cover bolts get tightened evenly to 41 N*m (30 ft. lbs) torque.
As another thought based on your symptoms, you might be better off letting the dealer try to fix it first (the chatter can be caused by various other symptoms as well, even though your diagnosis is probably right). If the dealer fixes it with the modifier, then you know that it is safe for you to go ahead and add your synthetic. On the other hand, if your problem remains or even gets worse after adding the synthetic, you may have wasted some good oil and might be inviting the dealer to claim the different oil as the cause. Just a thought, and if you need more details let me know.