read-
loaded truck and the weight of its attached trailer.
There are multiple limits on your truck. GCWR is just one of them. You are limited to what you can tow, based on which limit you reach first.
Lets say you're tow rating is 11000 pounds. If you had a hay wagon loaded up to that weight, you could theoretically pull it because every bit of weight is on the wagon wheels, and there is just a draw bar/hitch running from wagon to truck. Attaching the bar to your truck is like adding 20 pounds of payload.
Now lets rearrange that hay wagon. Take off the front axle. Instead of a draw bar, weld a solid hitch on the front. Suddenly you're going to be putting what, 5000+ pounds on the back of your truck because the rear axle is right at the very end of the wagon; the front will be supported by the hitch. You're still pulling the same weight, but you've transferred a horrendous amount on the back of your truck, so you can no longer pull that wagon. GCWR hasn't changed, but payload has. Now payload has been exceeed, it's game over.
Bottom line; when pulling a box trailer or an RV, these 1500s will always reach payload limit before GCWR limit. You're just wishing the problem away and only looking at what you can pull without regard for what you can carry. There IS a limit to what you can carry, and you will reach that first.
Other than hay wagon styled trailers, a boat trailer is perhaps the only other mainstream trailer you can pull that will allow you to hit GCWR without exceeding payload, because all the heaviest bits of the boat (motors) are over the rear axle of the trailer. An RV or enclosed/box trailer, not a chance.