7500 pounds dry = 8500-9000 pounds loaded. Loaded TW will be 1050-1300 pounds.
You mention that you are new to towing. You are planning to exceed GVWR and rear axle rating of the brand new $40-$70k pickup and $20k-$30k RV. Those people that do have experience and report on this forum towing a 7500 pound travel trailer with even the most capable half tons general are not comfortable on the highway.
I recommend a truck with at least 2000 pounds of payload and receiver rating of at least 1400 pounds when using a WDH, which is not that F-150. Whichever one is "cheaper" to change, I recommend it. For a TT, 6k dry is a good guideline for something like your F-150, which will likely still be over at least one rating with a family in the cab and a bed full of camping gear.
FWIW, my TV has 2050 pounds of payload, 9400 pound tow rating, but a relatively weak receiver @ 1000 pounds with WDH. I would not towing that TT, but I bet it would tow it more comfortably until my receiver breaks.