BK,
When I took delivery of the 3110, my 2010 F250 had no problems towing it home 70 miles. It did not feel overloaded. It did not squat the rear springs. The garage was empty and the fresh tank was 3/4 full thus making the fifth wheel hitch heavy. The air bags were later added to eliminate the rear spring bounce. The Firestone air bag kit was less than $400 and only took 3 hours for me to install. It greatly improved stability while towing. I have a crew cab, 6.5' bed, SRW, 3:55 rear ratio, non-locking, 2WD. I average 9.5 to 10.5 mpg while towing. I still have good acceleration while climbing bridges over the Mississippi River. This truck is my daily driver getting 15 mpg in town and 21 mpg on the highway.
However, when it comes to towing any of these big Cyclone toy haulers, I would be more comfortable doing so with a DRW. I would feel much better during a long distance tow. My next tow vehicle will be DRW, 4WD.
Your 2013 truck will do the job and you may be completely satisfied. Your towing capacities are slightly improved from my 2010. Your truck will not be overloaded. Your truck is rated for a 3383# slide in camper. The hitch weight of the 3110 will be much less than that. Probably between 2600# to 2850# fully loaded if you utilize your garage with some toys. I haul a golf cart - 1100#.