8200 pounds dry RV puts 99% of half tons over at least one of its ratings. Just for RVing, you'll add about 1000 pounds of stuff. If you take toys, that goes up a lot more. Without toys, I expect that TH would be 9500 pounds with 1250 pounds of TW.
You should verify your tire and loading sticker for as equipped payload as well as receiver rating. I agree with others that you will be closer to 1400 pounds of TW and 10500 with toys. You are correct that in theory any weight added behind the trailer axles decreases TW. Practically, that never happens for RVs unless you have a lot of weight behind the rear bumper.
You may end up spending some extra money than you planned. It may cost you $1000 deposit to change your order to a different model. Or it may cost you a lot more to upgrade the truck. Take your pick. I'd check with the dealer on applying that deposit to a different model. As for which one? Find out your practical RV limits (not tow rating) from above, as equipped payload and receiver limit. My guess is you'll want to stay closer to 6k dry, or less if you plan for toys.
BTW, I've never seen a pickup pull into a campground with an empty truck bed. Don't kid yourself. That's what it's for! Budget at least 200 pounds of dirty stuff.
