It's not clear to us right now what happens -after- the oxide punches through - clearly at high enough energy levels (voltages) you get more or less reasonable conductors again, but there's probably some sort of in-between that has information too. Now I'm thinking about low-amplitude square waves that slowly get bigger, with inferred resistance calculated with each pulse, and look for the change 'point' (or whatever).
Seems like I should be able to do that with a waveform generator with a big attenuator, and a triggered data acq. Interesting.
There are also a number of other tactics in play here of course, including some novel TDR work, non-linear junction detection (copper oxide made usable RF detectors before germanium was a thing, after all), and some inductive network analyzer experiments (sensitive RF detection keeps the voltages very low).