Interestingly, though I have read about these super high voltages, I cannot induce one. The highest I've seen is about 20V ish - and that involved a heavy impact. (As measured with 'recording' DMM and 'scope).You are over thinking this. A piezo disc will output over 90 volts if tapped directly. No amplication is required, indeed, you need to protect the ADC input with clipping diodes, but that is all that is required.
A microphone detects acceleration, which is what you have. A jerk detector detects changes in acceleration, which is what you want. NOT when a tik or tok occurs, but the difference between them from an arbitrary zero point.
I found a 'patent' for a 'Sensor for measuring jerk'. It's quite an interesting insight, but the application seems to be more about measuring changes in already moving things (worn bearings etc). If I hadn't seen your video, I would probably have intuitively guessed that it wouldn't work in a clock application...
Anyway, I built said "Jerk Detector" - (more-or-less) as instructed :-
With a 'cased' Piezo Sounder connected to one Scope input and the contraption above plugged into the other, I compared responses.
The Jerk Sensor was (almost) impervious to sound (apart from the loudest of handclaps) and produced a much larger signal than the 'cased' Sounder, in response to tapping the desk. The latter - while very insensitive, did respond to sound (handclaps, whistles etc).
I took my 'Scope to the clock (since I didn't want to disturb it) but wasn't able to pick up a usable signal from either unamplified Piezo
(This wasn't helped by the presence of an unwanted signal being received in the region of the clock! I thought it was perhaps a nearby zigbee Radiator valve, but disconnecting it made no difference. Very odd that the Jerk Sensor picked this up, but not the 'cased' Sounder (which just had some mains hum) - could just be a difference in scope probes I suppose ... or the excessively long leads ).