I agree with some others that a heavy 5th is preferable to a long/heavy TT. The weight being centered in the bed is a much more manageable place to carry it.
I ran a similar setup but about 1000# lighter than I'd estimate your loaded weight (2006 Duramax). I had the airbags which really helped out a lot. You've got plenty of truck engine and tranny wise. I ended up selling the 5th because of the downturn in the economy and having kids. When I got a new trailer I went back to a TT just for the simple fact of not having to completely empty and lose the storage in my bed each time I hitched up. If I got out more I'd opt for another 5th in a heartbeat. The way they tow is great and the floor plans are great.
See if you can poke around a bit and get a better idea of what the actual weight would be. If not this 5th don't give up the idea of one entirely. You have plenty of truck and there are plenty of nice floor plans that have loaded weights of 10-11000 lbs.