[Notanlines]

WhoDat, your 2500 isn't even close, so let's rule that out. The pin weight of your 5v'er is about 2500 pounds plus what you and Momma put in the front of the RV (Bedroom area?) plus what you put in the basement. That will be conservatively 500 more pounds. I know that doesn't seem right, but in the real world it will probably be heavier.
Now let's load up your new truck. #1 son, Momma, Dad and "Gumbo" the family dog will put about 500 pounds in first. 26 gallons of diesel fuel and a nice slider hitch and that's another 400 pounds. If we add up the weight in the bed of your new wheels you are in excess of 3900 pounds. At this weight you have moved in dually territory.
Keep in mind that I am not telling you that you are only going to be happy and only be able to pull your beast with a dually. But I am going to say that hands down a 3/4 ton pickup is NOT what will make you happy. You are in need of a 3500 SRW at a bare minimum. I might also add that the Denali just like Ford's Platinum is the heaviest of GM's pickups. Those little add-on play-pretties add up in a hurry.
You certainly WILL run into owners who pull your rig with a 3/4 ton. They are just wrong.