The folks who are already convinced that the 6.0L won't do the job... are probably right.
Your reported total gross combined was 11,372 pounds. That's how much some folk's trailers alone weigh... empty and dry. Then add the truck, the people, and the cargo, and the gross climbs up to 18-20-22K. That kind of weight on a 9% grade is going to be felt hard with a 6.0, which is otherwise an outstanding power plant up to 17K.
I currently own a 6.0/4L80E/4.10, and like the OP, feel that it hauls plenty. But if hauling more than 16K regularly on grades, then it is understandable to be convinced to consider other options.