Ghosting is caused by differential movement between the bed and the head when the head undergoes acceleration. The forces add energy to a resonance in that differential vibration mode.

By changing how you mount the base, you will change the mode and probably change the frequency.

With the soft mounting, the bed can move more easily. It will tend to follow the head acceleration better. The whole system will still ring (you can't get rid of the momentum change), but you can cause the energy to go somewhere else and not excite that mode.

With the base bolted down tight, the base gets stiffer, increasing resonant frequencies. You also may be making the base more resistant against racking or twisting motions.

It is completely credible that both interventions reduce the problem. Of the two, I would prefer any intervention that increases the stiffness.

If you know your movement speed (perhaps from your configuration file) and can measure the linear frequency of the ringing, you can determine the resonant frequency that is being excited. Depending on the frequency, you may be able to excite that frequency with an audio generator and transducer (maybe even just a speaker), such as with one of these: Dayton Audio Transducers.

With the system shaking at the right frequency, you can use your finger to find portions of the frame which are vibrating strongly, or maybe even your phone camera to make a high-speed video of the movement.