Snuffy,
I currently own a Bighorn 3500RL which is a slightly different floor plan but the weight ratings are identical to the 3400RL you are considering. We also have a 2003 Chevy crew cab Duramax and it pulls and stops very well. And with all due respect to Ray, I am not over the GVW of my truck. I had my rig weighed at the first Heartland Rally and my tow vehicle weight was 7,325 and my trailer weight was 13,375 for a total of 20,700 lbs.. Also, my pin weight was 2,050.
According to my Chevy owner’s manual (K-2500 Crew Cab Short Bed HD 4WD) the GCWR is 22,000 and the maximum pin weight is 3,000. The maximum towable coach is 14,700.
Having said all of that, I do agree with Ray that a dually would give a much better towing experience. I have always said that if I were to travel more extensively that I would get me a Big-Boy truck. Probably more on the lines of a Chevy Kodiak 4500, but I am just dreaming right now. As a side not I have recently added Firestone Ride-Rite air bags to my truck and will soon have a SuperChips tuner.
Good luck snuffy,
Mark