Mileage is ugly for sure when doing Red Mountain from Ouray to Silverton.
When I did it, driving "UP' the mountain and navigating the turns wasn't bad. It was the coming "DOWN" that bothered me. LOWER gear for sure! But, I still used the brakes and they really heated up and start smelling. I pulled off two times to let them cool down; and then travelled on. We were towing a 2008 Jeep Liberty.
I assume you don't have many miles on your brake pads, or you haven't done many mountain decensions to use/ride your brakes. If so, you may want to check the brake pads.
Happy and Safe travelling to you!
Pete and Patty
2010 Georgetown 378TS; 2012 4dr Jeep Rubicon
1 Yellow Lab (hers);1 Little Bitty dog (mine)