I towed all over Colorado, including Eisenhower pass with my previous 3.7 4X4 SCAB F150. Similar horsepower, but 3.73 gears and a 6 speed. We were towing a trailer that was around 4K lbs, very tall, boxy (lifted for off-roading and not an easy tow) and an ATV in the bed of the truck. On the Interstate, we were always able to go 65 mph, sometimes it was a 6500rpm, but I'm not one who worries about such things, put the hammer down and let the truck work. We were pretty much maxed out, but it didn't get hot, and it did the job.
My only concern with the Chevy would be the transmission, as I really don't trust the GM 4L60, but that's a whole 'nother discussion.