I don't know about the tow weight questions but can offer some opinions on some other things.
I'm buying a new truck and went away from Chevy (currently in an 06 Duramax) because the 6.0 is underpowered compared to the competition. I think it's rated around 360hp/375 torque. For comparison sake the new Dodge 6.4 Hemi is 410hp/430torque and Ford 6.2 is 375hp/400torque. These numbers are from memory but should be in the ballpark as I've pretty much been glued to the computer for the last month doing research.
I think Chevy offers the 6.0 this year with the 4.10 rear end to try and make up for relative lack of power. Fwiw, a buddy of mine tows an 8500lb TT with the 6.0 (3.73 axle though I think) and HATES it. It's a dog up any hills. With the weight you're talking I can't imagine you'll be pleased. Realistically, you are pretty close to diesel territory with 10-12K lbs.
To give you some comparison on prices that I've found, a Dodge Cummins Tradesman (fairly stripped down model but still a lot of options) can be had around my area for mid/upper 30's. 6.4 Hemi for mid/lower 30s. Those are both in 4X4 which is about all that are offered in my area.
Ford F250 XLT gas around 36K also 4X4 with some pretty nice options. I'd hope an outgoing 2014 Chevy with the 6.0 could be had for less than the comparable gas Dodge/Fords since it is lacking power wise but I'm guessing Chevy isn't admitting its shortcomings.
I stopped by a Chevy dealership and laid out my case for needing the higher HP/Torque to get out of my diesel and he didn't even pressure me if that's any indication. IMO for the time being Chevy/GMC can't compete in this truck segment. Diesel? of course but you'll have to pay.
Good luck.... lot's of good threads on here recently about new trucks. Do your research :)