"Hitch rating is 10,000 lbs. I've looked into the braking and towing set up. Company said they run about $3,000."
$3k seems like a lot, unless that's all costs including install for anything on both vehicles.
I think I got away with the install on my Dodge Dakota for right at $1600 for all (Brake Buddy, Base Plate, Tow Bar, Lights).
I think that rig should have no problem towing that truck, it weighs about the same as my '08 Dakota CC 4x4 (gotta love the aluminum weight savings of the new F150) and I tow it with a 34' Class C with a gas 8.1 V-8/Allison Trans, and it drags her along without much of an issue.