I have an 18 Platinum 3.5 EB with Max Tow. 1557 payload and with my 28' Coleman 274BH hooked up I have 400 pounds reserve payload. I use a Blue Ox and the trailer pulls smoothly and steadily. It falls around 6400 pounds loaded for a two week trip with a full FWT.
If anything, it gives the OP an idea what Ford has that can tow what he has and more. Mine is the 145" WB. The XLT and 501a Lariat models will have more payload, 1800+ and there is the Unicorn if you can find it, the HDPP model with up to 2800 pound payload in the XLT trim. The downside of the long WB is that they are difficult to park due to the wide turning radius so would take some getting use to after driving a car like Tacoma (my F150 steers car like too, so not a slam).
Oh, it also gets 24 MPG highway when not towing.