Because it has an aftermarket tranny cooler, then it probably did NOT have the factory towing pkg, which included a bigger radiator. So the first step is to be sure the engine fan is working as designed. If the fan is doing its job, then I'd probably save my scheckles until I could replace the radiator with the biggest one that will fit.
With the new radiator, never use tap water. Flush with distilled water, then add enough concentrate antifreeze to be at least half the total capacity of the cooling system (but not more than 70%), then top off with distilled water. Do no use ready-to-use (50/50) antifreeze for a fresh fill, because you'll wind up with less than a 50/50 mix. (Some of the distilled water you used to flush the system won't drain because it's in the block and heater core.)
Grumpy ole man with over 50 years towing experience. 2012 F-150 Lariat SuperCrew EcoBoost, 6.5' bed, Platinum White/tan, Leer 100XQ camper shell, Nomad Joey 196S TT, CarMate 7x14' enclosed cargo trailer, three other utility trailers, plus a retired 2000 Keystone Sprinter 25RKS 5er we rarely tow now. ProPride hitch on the TT. Reese Strait-Line hitch on the cargo trailer.