Sounds like a really nice trailer. You may be a little over on the payload with the F-250, but maybe not because you have a gas motor.
That size trailer will be at the limits of what a gas truck will tow. Some will tell you to sell the truck and get a diesel or buy a smaller lighter trailer because it may just roll backwards when it sees a hill
. I would not hesitate to that trailer with a newer gas motor and the 6speed trans.