The F-250 and F-350 are basically identical, except that the SRW F-350 has a 11,500 GVWR, and a 4,000 pound cargo rating, and heavy duty rims and tires, leading to a 6,500 pound rear axle weight rating.
Yes you need the F-350 SRW, if not the dually.
Have you already installed a water coolant filter? You should have one, it will prolong the engine life a LOT. Napa #FIL 4070 is the filter part number, while FIL 4019 is the mounting kit to install it inline with your heater hose, and when the heater stops working, get a new coolant filter.
Fred.