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HD is a smog emissions term and has nothing to do with towing capacity. Anything with a GVWR above 8501lbs is "heavy duty" according to the EPA. Your problem is that the truck is too heavy for the engine. There is not that much left of the CGWR for the trailer. It is not a safety issue as far as tires, bakes, frame, etc. because they are independent of engine size.
If that chip really adds 27ft-lb and if it is at a low rpm (probably not), then it should let you tow a little more trailer weight. By all means get the biggest trans cooler you can find for that E4OD!
What are your terrain conditions? Sea level, level ground, or high altitude and steep grades? How slow can you stand to go? What kind of distances do you plan to tow? Use some common sense judgement.