A 6.2 with 3:73 gears at 60 mph in 3rd gear is nowhere near redlining so that's not a problem. I'd think that 3rd gear at 60 pulling a steep hill would be better than 4th because the torque converter would probably be locked.
I put mine in cruise and let it do it's own thing because I don't see any problem with doing that but I haven't had it over the Rockies yet. The sweet spot with my 6.2 litre and 3:73 gears seems to be about 63 mph. I'm pulling about the same load as you are.
I've always heard the expression that "there's more than one way to skin a cat" and I believe this applies to your situation. Try it different ways and see what works the best for you.