In Louisiana you now have to register your truck based on GCVR not GVWR. So my 2000 F250 is registered for 20,000lbs. That is what Ford stated for all 2000 model F250's and F350's for that year. Every state is different. We now do not have to have single axle trailers or boat trailers inspected new rule.
Sounds like you have a fuel pump problem. You were running 60 mph and shutdown with no slowdown or cool off period (pulling in gas station or parking). Oil and engine at temp at this point it will get hotter for about 15-30 minutes then start cooling down. Check all grounds and change pump and filters problem should be corrected. While you have the pump out drain and wipe out fuel tank. I have seen the heating problem several times. I have checked several vehicles with a thermal camera and infrared thermometer.
I have rechecked with Louisiana DMV and at this time there are no requirements for towing a motor vehicle by a private individual in Louisiana, only tow companies. Trailer rules only apply to trailers per the State.