Do you have a transmission temperature gauge?
The transmission will get pretty hot at 4000 rpm in a lower gear. Don't worry about holding highway speeds. Go slow, things will be easier on you and your truck.
Does your truck have a factory towing package? If not you should consider adding a transmission cooler to the truck.
Going down a hill is a whole lot more dangerous than going up. We tow with a Chevy 2500HD and DuraMax/Allison. Our rig grosses 20,500 pounds. Here is what we do when we see a steep downgrade (6% or Better). We slow to 52 MPH, manually downshift to 3rd gear, set the cruse control, and let the engine hold the rig. If we have to apply the brakes we apply light steady pressure. The key to getting down the grade is to get control before you start down.
Jane and Chauncey, Plus the Cats: Backslash, EB, Stripes