Thinking out loud here.
What's happening to cause excess bouncy feeling is resonance between the suspension and the bouncing bike rack. Even a small input from the road at just the right frequency makes the whole system move a huge distance.
Technically he could fiddle with the damping (or spring rate) on one end and change the frequency that resonance of the system occurs at. Or throw metal at the bike carrier so it is less springy. Or make the carrier shorter so there's less moment arm. Or use a different material for the carrier. Etc etc etc. If you can make changes to move the resonance to the correct frequency range, the issue goes away completely for during 'normal use'.
The trick is, if you mess with the suspension, you're messing with how the motorcycle handles, not just the resonant frequency. Ah the joys of 'tuning' a chassis and suspension...
