Don't be affraid to let it run at high RPM. You wil not kill an LS based engine doing that. I am going to assume you have no warranty. What are the miles?
If you are that unhappy spend the money and get a tune. It will be a night and day difference elimante torque management and change the torque converter duty cycle.
I have been towing 7500 lbs (combinded weight scaled of abou 14200 in my 02 6.0/4L80E/4.10s for the past 7 years and even here going over places like Vantage, Lookout Pass, 4th of July Pass, The Contiental divide I have no trouble going 60-65. Even in the heat coming up Vantage I let the truck settle out bewteen 3800 to 4400 RPM which is usually anywehere from 55 to 65. I had the truck tunned locally 8 years ago and it made a huge difference. I also put a larger tranny cooler on to account for the change in torque converter duty cycle. Since my 02 has just over 55,000 miles on it and is just for towing it was cheaper and easier than getting a new truck. Thing about the 6.0 is maybe slower than some other trucks but it is rock solid reliable.
I might add my truck is light for a Crew cab long bed 3/4 ton. It has no options but A/C and cruise. It is also 2WD. With me, and a full tank of gas it is 5890 on the scales. With the family and camping stuff it about 6500lbs.