I agree the 3.73 gearing will be more than adequate for the load you are carrying. My father had 3.73 gears with a 7.3 and he hauled a 16,000 pound FW for about 50k miles with it. So you will still have plenty of power for the measly 2000 camper.
On a side note, lifts and campers don't go well together. Before you invest in the lift, see how far you can go first. Make a few trips with the camper and see if you need the lift to go where you want to go. I had a stock F350 Crew Cab and always surprised folks on where I showed up. Also, make a spacer for the bed and put the camper on it. You may be surprised that the extra height makes the rig unstable enough that you won't be able to take advantage of the lift anyhow.
Lastly, unless you have talked to Four Wheel Camper about the construction, bolting it to the bed may not be strong enough to withstand the rigors of even easy off roading. The bed flexes a certain amount and the camper is designed to be basically rigid. With spring loaded turn buckles, the bed can flex a certain amount under the bed.