To some extent, I think what you're experiencing is typical for a
light, short, tall trailer. Increasing tongue
weight helps. Increasing overall
weight also helps. Ours is smoother when packed for a trip than empty. Of course, I wouldn't pack unnecessary items just to make it heavier!
Sometimes changing speed helps when regularly-spaced road imperfections (expansion joints, for example) cause a resonant bounce.
Make sure you have eliminated all slop in the draw bar connection to the receiver.
I'm assuming the updated
axle is appropriately rated for the actual weight of your loaded trailer. That should mean it is tuned for around 2000 pounds.