I also had chucking when we first got our Jayco. I added a 5th Airborne pinbox and shocks to the 5er.
Yours is not a really heavy trailer but as mentioned, you should check weights. Make sure it is towing level. Make sure there is no slop in the hitch. It is unfortunate that you spent money on the hitch before trying out the rig first but with some adjustments it should be OK.
As for shocks on the trailer I beleive that rig has the rubber torque suspension. Not sure if it is easy to add them.
Best of luck in your quest.