Well what is the GVWR of the F250, Ford and pushed their 250/2500 past the established 10,000# around 2020 or so.your loaded weights add up to 11,540#.
If your GVWR is less than that, along with exceeding the rear axle rating, could lane you in legal limbo if involved in a crash.
I towed about 13,000# with a 2001 Ram 2500 CTD with a 8,800# GVWR and a 6,084# rear axle rating. While I was within axles, I was 1,700# over the GVWR. While it towed great that nearly ton over GVWR got to me, and got the 2016 3500 DRW. The only change to the TV was Bilstein shocks.