Just some food for thought. My 2012 5500 has a 19,500 GVW. As it sits without any chips it weighs in at 13,500 That leaves 6,000 lbs for chips, with a 14 yard box. Chipper weighs in at 7,000 lbs... truck will do the chipper and load of chips without too much fuss. A few of my friends just bought 3500's with 9' dump beds, they have 13,500 GVW. A 12' box is going to carry at LEAST 14 yards, little bit overweight for a 3500.
As far as rated towing capacity... I spoke with a dealer one day, told him that I had just pulled a 12K excvavator on a friend's trailer for a total haul of 16,500 plus the truck... he was impressed stating that I had just pulled 30K (this of course included the truck)... just food for thought.