You are over thinking this. You will be fine. Personally I prefer LT just due to the stiffer sidewalls,but your rating will handle anything you can hook to your truck
Your axles are used in many different applications so their rating may be differnt from one to another.
Millions hook to travel trailers every year, billions over the decades. Our highways are not strewn with death and destruction wrought by dangerous RV'ers. Hell my grandparents towed a trailer across the country with an 85 hp buick. In the thirties my grandpa toured the nation hauling a merry go round behind a Model T truck.
This ain't rocket science folks!