Great work on the clacker. It seems to be fast enough to generate repeatable experiments while clearing momentary shorts. The piezo actuator I suggested might be used to increase the repetition rate, but that could be a future enhancement if it seems worthwhile.
Regarding your earlier question:
First test results with the cell empty of liquid. With the inductor steel core removed, peak-to-peak voltage of 538 volts is seen, with resonant ringing at 5.8 MHz. With the core inserted, the peak voltage is slightly lower and the ringing frequency is higher, at 6.4 MHz and is more quickly damped. This is counter-intuitive, as higher inductance should result in lower frequency.
The oscillation frequency depends on both L and C. If modeled as lumped L and C , F = 1(2*pi*sqrt(LC). When you add a core, it increases both L and C, which should decrease the frequency as you say. The way I think of it, is that when the clacker opens, you have an energized un-terminated transmission line where the propagation delay determines the transmission time and hence the resonant frequency. You can also think of it as an antenna that resonates at at frequency of about 6 MHz.
At 5.8 MHz, a quarter wave antenna would be 40.3 ft (484 in).
At 6.4 MHz, a quarter wave antenna would be 36.6 ft (439 in).
The electrical length would include the leads to the anode/cathode, the wire in the inductor, the wire to the supply, and the internal wiring inside the supply. Could any of that have changed between tests? Could some windings have shorted out when the core was inserted? I doubt that the core had a very large effect on the inductance without a closed magnetic path and something else must have changed in the other direction.
If you do not have an LCR meter, you could measure the inductance easily with your scope. Temporarily put a resistor across the inductor (say 100 ohms). Then run the clacker outside of the electrolyte and record the voltage waveform across the parallel LR. The clacker shorts to charge the inductor, then opens and the inductor is discharged through the resistor. Measure the transition time for one time constant (63% drop in voltage). Then L = t/R. If you measure inductance with and without the core, it would help to understand the mystery. That would also help us build an accurate SPICE model of the experiment. While you are at it, measure L with a steel C-clamp clamped between the ends of the bolt to provide a low reluctance magnetic path. That should result in a big increase in inductance.
(Another way to measure the inductance is to use your signal generator to drive a square wave to the inductor through its internal 50 ohm source impedance.)