I live here. 15 minutes from the pass and the tunnel. Unless the tunnel is closed, which is very rare, use the tunnel. The pass is considerably higher, sharper corners and much steeper. The pass is often closed periodically during the Winter because of snow and ice and the HazMat trucks must wait on the hour so the tunnel can be closed for a few minutes to allow them through and maintain safety for the general public. You'll have relatively steep ascents at Mt. Vernon just West of Golden/Lakewood. Another on Floyd Hill. The short and very steep climb from Georgetown up to Silverplume. The short approach to the tunnel. The long and winding road to the summit of Loveland pass if you go that way. The descent either way with the tunnel descent being relatively straight compared to the pass. The climb up Vail pass. None of which should present a problem for you or your truck and load. The best way to preserve your brakes is not to allow yourself to get going too fast in the first place. I don't know how your truck is configured and how the Tow/Haul works in it. The Tow/Haul for mine generally keeps the transmission from constantly shifting to keep the temperature down. Adjust your electronic trailer brakes to balance the braking between the truck and the trailer. Make sure, and this is a big one, make sure your trailer brakes are adjusted correctly and all work. Grease the wheels. I've had trailers where only three of the four wheels brakes worked so test them by raising each side hitting the controller manual override (you'll need someone to help) and make sure each wheel locks up when you try to rotate it. Have fun, some nice scenery along the way.
Oh, to your question, put it in Tow/Haul and let the truck decide for itself. The computer will decide based on load, throttle position, rpm, speed and keep you in the best gear possible.