The way I read it, the hitch was low, so the trailer was riding nose down, which would force it forward into the hitch. Like that, it wouldn't chuck back and forth (as much), so it "seems" OK. Setting the hitch higher and getting the rig level now allows it to move slightly in the jaws and now it's chucking on stops and take-offs.
Riding nose low or nose high affects aerodynamics, as well as load distribution on the trailer tires, so you want to be level. To eliminate the chucking will require changing the pin box to one that dampens it (5th Airborne, MorRyde, etc.) or getting a hitch that has dampening built into it. New pin box would be less expensive, I think.