Your in solid DRW territory. I'm in the same weight class as your looking at. I'm doing it with a class 4 (2012 F-450) and it's comfortable. Not sure I would want anything less (and there aren't many lesser trucks that can do it within ratings). My GCW is 31,300lbs. There isn't a Ford SRW that has the ratings to handle it. Here's the details of my combo, hope it helps you.
TV - 2012 F-450 Lariat Ultimate package FX4 CC DRW 6.7L Diesel (400HP/800 ft-lbs Torque), 4.30 axle ratio, 6sp auto/manual tran with Engine brake, Firestone Ride-Rite airbags / Air Lift WirelessAir compressor and controls, factory 5th wheel prep, 25k Pullrite OE Super 5th hitch, 13,300lb GVWR, 24,500lb 5th wheel tow rating, 33,000lb GCWR.
5er - 2008 KZ Inferno 4012SL Toy Hauler, 43ft length, 18,000lb GVWR
TrailAir pinbox, Trailair Equa-Flex suspension.