You can simulate a little help from a suspension aid real easy.
If you have time, do this.
Cut some wood wedges or buy 4 hockey pucks or plastic felling wedges.
Insert them in your leaf pack above the bottom overload spring. So the springs get into the overload as soon as load is applied. Secure with hose clamps or even a good cinch with baling wire/tie wire.
That will stiffen your rear suspension under load.
Leave the wdh at home. Hook up and take a spin down the highway. Will give you a good idea what Stable Loads/helper springs/air bags with moderate pressure would do.
Stiffer rear springs will reduce the bounce you’re feeling.
Again, your truck is 100% capable and safe, actually ideal, for a trailer this size.
If you want send me a PM and we can talk. That trailer should pull like a dream with only minor tweaks.