[JRTJH]

I think the "simple and unsophisticated answer to why" is this:

Ride comfort is a result of suspension travel and damping.

Suspension travel and damping are a result of tire sidewall flex, spring movement and shock absorber damping.

In a car, 28-34 PSI allows increased tire sidewall flex.
Long leaf springs or tall coil springs allow for more spring travel which absorbs "jolts".
Shock absorbers dampen (cushion) much of the remaining "jolt" sensation and the result is "smooth riding over bumps:

In a truck, 80 PSI and thicker ply sidewalls do not allow as much sidewall flex.
Shorter/heavier leaf springs, undampened overload springs and stiffer coil springs cause more "jolt sensation" and less suspension travel.
Shock absorbers dampen as much "jolt" sensation as they can, but the required payload capacity in HD trucks causes a necessary "road feel".

Most HD trucks that I've driven or rode in do feel "rough on bumpy roads" when empty or when lightly loaded. That same truck, when loaded to capacity, rides much smoother over the same road.

Now, given your "dually with high tire pressure, light tongue/pin weight trailer and "barely perceptible load configuration"... It's no surprise that you are feeling every bump in the road...

As for things you can do, first weigh your rig, find a tire chart and adjust your tire pressure to the "true load" not the "door post sticker recommendation"..
Next, consider Bilstein shocks and/or/and supplemental air bags
Third, go ahead and get that bigger trailer, load up your dually to "near capacity" and enjoy a more comfortable ride (if you slow down on bumpy roads).

Alternative: As flybouy said, find a travel agent, book your flights and pray for clear skies with no thunderstorms along the route....