Not sure what year model your truck is, but there are two types of radiators for the 2011-2014 3.5L EB F150s. There was a standard 41 row radiator and a "super cooling" 51 row radiator that came with the max tow package and also came standard with all 6.2L V8 engines regardless of towing package.
Also, being at lower rpms with a lot of load will dramatically increase EGTs and other temps including coolant. Did you try dropping down a gear? I know the 3.5L EB likes to hold highest gear possible because it has enough low end power to so, but that may not always be the best thing to do. Dropping it down a gear to be in the 3,000+ rpm range has worked for me to reduce temps on a long climb. The same goes for any turbocharged engine, even diesels.