In short, no.
More...Assuming it is the normal sheet metal bumper that is just barely welded on, I would not do it. You are raising 2 issues that should be addressed. The integrity of the bumper and changing the hitch weight. The bumper "could" be modified with trusses and more weldment. But it is still a paper thin bumper. Plus, Keystone "may" deny a warranty claim if you have frame issues because of the modification. The other issue is the weight. It will not be a 1:1 ratio of adding weight to the rear and removing that same amount from the hitch.
So, I would say don't just hang that weight on that factory installed bumper. You may be able to find a receiver hitch that welds or bolts to the frame rail at the rear. I would discuss that with your dealer.
RV Receiver:
http://www.curtmfg.com/Search?term=rv+receiver
The quickest easiest solution? A front receiver hitch installed on your truck and a cargo basket:
http://www.curtmfg.com/Search?term=front+receiver
Cheaper from Amazon.
Have you weighed the rig and calculated the pin weight, or are you looking at the "squat" of the truck. Looking at the 5th specs it shows 1480 pin weight. I bet you end up close to 2200 all loaded up and ready to.
You ever hang out in the Superstitions? I need to poke around there some. Infamous relatives: The Hermit and the Baron.