Aha. In passive instruments, the controls and the pickups can interact in ... interesting ... ways.
A pickup has inductance, capacitance, and resistance. This combination gives a pickup a characteristic damped resonance. (Alembic filters do much the same thing, but twist a knob or two, or flip a switch, and the characteristics can be changed to almost anything you want.)
In the most common way of wiring controls in a passive bass, the volume pot and the tone control become part of the resonant circuit of the pickup itself. They can change the frequency and the damping (Q), not always in a desirable way. Adjusting the volume and tone controls can interact and affect this, not necessarily in a very intuitive way.
Without hearing the "clack" you were fighting, I'll just venture a guess that some of the capacitor values you tried created a resonance at a frequency that did not flatter your pickup.
If you're inclined to continue experimenting with different capacitor values, try turning the volume control down just a little and see if the clack goes away or changes.