I have a 2012 Ram 1500 pulling 5000lb trailer. The Ram has "tow package" and a tow-haul switch on the instrument panel. We just came home from a route which had us climb up and down several steep grades. With the tow-haul switch "on" the engine helped gear me down automatically. I still needed to brake sometimes but the engine gearing down really helped. If you have a tow-haul type switch on the Tundra I would use it and not worry to much about coming down a steep grade.
Not being familiar with roads in and out of Wyoming I can't help with that issue