We pull a White Hawk 20MRB with a 2008 Explorer Sport Trac with the 4.6. There are differences between our tow vehicles such as the tranny, 4 speed vs. 6 speed. The 20MRB gross is 5900. Currently, it is about 5600 loaded. The Sport Trac has ample power but what concerns me with your TV is the F150 weighs more than the Sport Trac and my GCVW is 500 pounds more than yours.
I think you can haul thr 23MB but it won't be a fast pull up hills.
Real life experience as we are currently freezing here in Arizona at 5600 feet. The trip yesterday was uphill with a good headwind most of the day and at the Continental Divide is was over 7000 feet. Only dropped it to third gear a few times and crawled at 40 mph.
Good luck in your pursuit.
2015 White Hawk 20MRB
2011 F150 Non EcoBoost (5.0)