My nature is to try to do things economically
so first thought is to think of any of your friends who
have a Ram with smaller tires
and see if they would swap with you for a weekend trip
so you can 'feel' the effect of the smaller tires.

The easiest way to climb hills better
is to go to tires with lower rolling resistance that 'frees up' some horsepower (tires vary a lot)

If these tires are smaller diameter this will allow the engine to generate a little more torque at higher rpm....but the 5.7 Hemi has a pretty flat torque curve from 2000 - 4200 rpm

If you are trying to climb hills at low rpms 'effortlessly' a gasoline engine really can't do that like a Cummins Ram can.

The 5.7 Hemi needs to be in the 4200-5400 rpm range to 'give its all' in hill climbing. This is gonna be noisy and with vibration.

Have you tried manually shifting down to 2nd gear before getting to hills?