If you better define drive the heck out of it and mash the gas, we can make better recommendations. What is your cruising engine speed on flat ground and what does the engine turn on these hills? Your engine makes its peak torque over 4000rpm. Lower gearing/higher axle ratio will help get and keep the engine there, but you still need to understand how much that will help. You won't suddenly be able to tow at 2000rpm up mountains.
Towing any high walled RV is hard work just to pull two sheets of plywood through the air at 65mph. You should be towing in 3rd gear most of the time and with tow/haul mode. Hills/overpasses will drop speed. When I had a similar powertrain, I let the vehicle speed drop to about 55mph before I downshifted to second gear, which would be 3800rpm. And that's was with 3.73 axle. You have two accelerating gears and one cruising gear. The truck will do it all day long. You as a driver may not like it, so changing gears may not be satisfactory. IF you want to never exceed 3000rpm for example, you need a vehicle that has significantly more power under that. A Big block or forced induction will do that, like Ford's Ecoboost or a diesel. If you have 2WD, change the gearing to 4.10 for $500 and see if you like it. Otherwise, save your $ for a more capable truck.