I have a 3950 Cyclone HD. I pull it with a 2008 F450. If I recall the advertised pin weight was about 3100-ish pounds. I have a pin weight, ready to roll with reasonable "stuff" loaded, of 4,300 scale verified pounds. I'm guessing your truck is going to be over its factory rating by at LEAST 2000 lbs.
Will your truck pull it? Sure, but getting the load rolling is the easy part. Will your axle actually handle it? Not sure but probably so. My rear axle is rated by Ford at 9,500 lbs. It's rated by it's manufacturer at 14,500 lbs. Why the difference? If I had to guess probably a couple reasons. Conservative rating by Ford for warranty/liability issues, the axle might handle it but maybe the brakes won't, frame capacity etc.
Some guys tend to take each component as an individual entity and forget that it's part of a whole package and things are rated so that the whole package can live a nice long life, not just pieces of it.
A guy pulled into a campground where I was staying pulling the exact same model camper I have, pulling it with a 3/4 ton truck. He had no clue his campers over all weight and no clue as to his pin weight. When I clued him in his reaction was no wonder his truck laid right down to the bump stops when he picked up his new toy.
I'm not the weight police. It's your skin and up to you how you risk it, and your equipment. Matters not to me. "I" did my homework and bought a truck I knew would handle what I wanted to buy, and I wouldn't have to have these kinds of worries.
Good luck and I hope things work out for you, whatever you decide to do.