Based on my experience you should be able to tow that trailer. You will likely be right up against your payload ratings depending on how much stuff you take along.
Our Jayco 28U is 5400 lb as shipped. The trailer cabin is 28ft. Overall it is 30.5 ft. Loaded for snowbird travel it is 6600 lb. My truck is a 2012 Silverado crew cab 4x4 5.3 6spd 3.42 rear end. We use and Equal-i-zer 4 point hitch. I am at payload limit.
We have done round trips from Ont to Maritimes, Key West, Malibu, San Diego and are currently at Lake Havasu this trip. Mileage is way over 30 000 miles towing.
We get no push or pull from transports passing. When going up long steep grades the engine does rev - up to 4000 at times. Those engines are built to take those kinds of rev.
The 2016 has 355HP vs my 315. I don't remember torque. Did the 2016 come with the 8 speed? That would likely help on long hills.
Would a smaller trailer be easier to pull? Maybe. However fuel economy would likely remain about the same since it is the windage of pulling the box through the air that is the real penalty. Now I don't have any experience going through the Rockies.
It does depend on how comfortable the OP is driving a long machine. Some people as mentioned above will never be comfortable. Others are fine.
However, being reasonable on what is loaded and how it is loaded that truck should work fine.