My 3100 dry weight camper is well over 4,000 ready to camp. I used to carry it on a SRW 3500. I switched to a dually. Driving out my garage, down the drive way, and onto the highway was far enough to tell a huge imporvement in bounce and sway with the dually.
Could you make a SRW work with that load? Probably if it's a fairly new truck (2011 or newer) and you spent lots of money on 19.5" wheels and tires as well as other upgrades.
I'd get the dually. You'll still probably be over the GVWR of the truck. Most people with TCs are.