Hello OP,
We tow a TT with 4600 lb dry weight and estimated ~6000 lbs fully loaded. My truck has a 4.7L V8 (1st gen Toyota Tundra), quad cab, 4.10 gearing, 6600 lb max tow capacity. I'm a bit over on GVWR, but with the WDH it sits level. We've towed from Montana to Oregon and back and pretty much any local camping trip involves climbing mountain passes. I am the guy going 45 mph up the passes with hazard lights on, but I'm fine with that because the big rigs are doing the same (sometimes I even have to pass them!). Now for sure I'm often day dreaming about the next truck that will tow this TT without breaking a sweat, but I'm not in a hurry to buy something just so I can keep it over 55 mph on the passes. Now I'd want a test drive/tow before I committed to anything, but I wouldn't be nervous about the setup you've described.