Hi,
You have a 2500 series TRUCK! Not some little 1/2 ton thing that should not be towing 11,000 pounds. The trailer is only in the 6,500 pound range. I would guess that you will have electric brake controller. Without the electric brakes, yes kiss your self goodbye, that would be crazy!
Leaving it in the tow haul mode, then lightly tap the brakes at the top of the hill should downshift it a gear. Then compression braking should handle most of the speed that can build up while going down a steep grade.
Yet you never mentioned going through the Rocky Mountains, or down any well known 11 mile long 7% steep grade, just a short run on the freeway. What you are planning is pretty simple. A truck rated to tow and stop a 12,000 pound travel trailer (with electric brakes) and you will only be towing about 6,500 - 7.000 pounds. No big deal at all!
Fred.