3.21 should be fine on a 5.7 with variable valve timing and an 8 speed trans.

I changed from the factory 3.55 to a set of NOS 3.21 gears when i had to have pinion bearings replaced at 65,000 miles on my 1995 Ram 5.9 V8.

MPG went up by 1 at a steady 60 mph on an unloaded truck.

3.21 diff in 2nd gear ratio of 1.45 on the 46RH actually is a better towing hill climbing ratio.
It would be even better if the TCC would lock up.

3.21 diff with 1.00 third gear ratio gives slightly better MPG on the highway

But 3.21 with 0.69 overdrive while towing is an even worse chance to take than overdrive towing with 3.55