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.
You are likely to overheat the windings in your alternator. Alternators are not designed to run with a heavy load for extended periods of time. Also the bigger the load you have on your alternator the harder it is to turn and is rough on belts and pulleys and wiring.
I connected our camera to a running light. Headlights on camera on lights off camera off. Power is already at the rear of trailer for this easy to connect. Works for us as I always tow with my headlights on.
Lippert sells a Goosebox. I use a Colibert adapter with no problems. Check the link below it is from Lippert the frame manufacturer so there should be no problems using it.