In my opinion, don't over think things with the gear limits. I don't remember the weight of my travel trailer, something like 3500-3750. I will use tow/haul mode and just put it in drive. Even going down hill you shouldn't down shift it. The 3.0 Duramax is equipped with an exhaust brake that works automatically based on brake pedal application. Leave it in drive and just gently apply brakes when descending hills. The transmission will automatically downshift and the exhaust brake will engage and you can release the brake pedal.
My biggest advice is keeping an eye on DEF. The gauge is a range estimate (much like "miles to empty" for fuel) so it will move drastically if vehicle usage changes. The 3.0 will use a lot more DEF when you work it hard, so it is good to be prepared. Once you get familiar with what your usage is like when towing, you'll know if you should bring a jug with you.