Your math is right from the info you have. Actual measured weights are so much better. Use the values from the maker's stickers in driver door frame for max limits.
Loading the truck up as if going camping with people and stuff and getting it CAT (or other) scaled is simplest but you can get the truck weighed empty (if more convenient) and add expected weights from that and be close.
Careful loading and shifting balance in the TT can get your tongue weight where you want it.
I also recommend downloading Ford's Towing Guide for your model year. You can cross reference your truck wheel base, cab type, engine, rear axle ratio, type of factory towing package (if any), and find your factory towing limit.
When I had a lesser tow vehicle, 2008 Ford Explorer V6 with towing package, I cleaned out a lot of excess weight from normally carried stuff from both tow vehicle and trailer to be under my rear gross axle weight rating. Because when CAT Scaled, I was overall within GVWR & GTWR & GCWR, but I was slightly over my TV rear GAWR without the WDH and slightly over my TT GAWR with the WDH!