Here is my opinion. Chucking forces are generated by your trailer. As the 5er goes over a bump it creates a rolling motion on an axis between the two axles. Due to the angle created by this axis and the height of the hitch this rolling action is translated into up and down forces and back and forth forces (chucking). The greater the angle (shorter trailer) the more fore and aft forces relative to vertical forces and the greater the chucking. This is why bumper tows have no chucking as the angle is small due to hitch height and the forces are all vertical.
A standard fifth wheel hitch is a solid joint between the trailer and the frame of your truck. This is why you are feeling it in your cab. The solution could be two fold. One, reduce the rolling motions with better axle equalization or trailer axle shocks. Second, isolate the fore/aft forces from your truck with a rubber isolation pin box (MorRyde), air suspension pin box or air suspension hitch.
The forces generated by the truck tires going over bumps and being transmitted to the frame might be mitigated by better shocks, Timbrens, air bags or a bigger truck but the chucking forces are coming from the trailer. A hitch with tighter jaws may be quieter but would be better at transmitting chucking forces to the frame and therefore to your seats.
I've been exactly where you are and tossed money at the truck fixes with no results. Chucking was eliminated once I isolated the trailer. Good luck and have fun with your new 5er.