Hate to do this on my first post, but I should bust your bubble before you bust something else more expensive.
I was a mechanic for years, and can tell you that the numbers advertised from the manufacturer are inflated so that they "compete" with other trucks inflated numbers.
Yes. Your Avy can tow that trailer. My F-350 can pull 60,000 lbs under the right conditions. However, your tranny and rear end aren't build to withstand it for too many miles. If you never plan to run any real distance and will not be pulling it often then it might be worth the gamble, but I'd give you 50/50 chances of a one way cross country trip without a major failure.
being within 100 lbs of any of the suggested ratings is cutting it way too close. You should also keep in mind that the brakes on that Avy are sub-standard for towing. In my opinion... too much trailer for that truck.