Your current truck has a max payload of 1585Lbs.
My calculations has your truck towing a max loaded trailer at 6200 Lbs.
That puts 806 Lbs on the hitch. Which leaves 779 Lbs for passengers and cargo
before overloading.
Now the F250's have a payload of between 3-4K depending on cab/box features.
Lets use a F-250 4x2 Crewcab shortbox Diesel with a max tow of 14000Lbs and
payload of 3540Lbs. The limitation becomes max tow since 13% hitch wt of 14000
is 1820Lbs Well under the max payload of 3500Lbs.
Combined with your Eagle324BTS loaded up to 9500Lbs and hitch weight of 1235Lbs,
you'll never worry about what you can and can't carry.