You might need to add some foam under the piezo to improve damping.
If the wires from the piezo disks to the Universal controller are long or are routed next to heater or stepper cables you may be getting interference.
Finally, with the mass of the bed providing inertia, you need to do everything you can to reduce the impulse when you start homing, even though your bed is not moving. Reduce instantaneous speed change for Z to zero, at least during probing. Reducing Z acceleration will also help. This should allow you to set the trigger threshold closer to the resting value without getting spurious triggers, improving accuracy.
Idris