I don't see the sparks?
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it actually doesn't act much like a diode as far as small signals are concernedWhat is "a diode"? Two bits in one bulb.
_I_ would say the vacuum diode is the better _rectifier_.
But when building a "clipper", you want an ideal diode PLUS a voltage. The fault of crystal diodes as rectifiers is a large built-in voltage. If this voltage is suitable for your clipper, the fault is a feature.
Cooling the cathode works (I'm sure you know) by lowering the average emitted electron velocity below zero. The high-tail of the gaussian curve can be urged to leave the cathode surface by some "large" positive voltage on the other electrode.
This is also the cause of DC error in tube DC amplifiers. Diff-pairs tend to cancel, certainly good enough for 1.5V VTVMs. More sensitive tube DC amps often sport regulated heater supplies (an awful expense in those days).
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The tube used. I've never seen them beforeSmall twin-diode. THE way to demodulate FM. The standard AC-DC converter for VTVMs. Sometimes used in AM/SSB for detection and AVC or for (duh) clippers to tame ignition hash and other impulse noise. I have seen it used for B+ power supply for very-very small gear.
But the exact tube used is NOT a key detail. Take any isolated-cathode twin-triode. Tie each grid to its plate. It is now a twin-diode. Obviously it should cost more; in today's world you can buy 12AX7 on a rainy saturday night in a distant town, or may have a stash of odd-sounding 12AU7es which just might be groovy diodes.
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Do you intend to add a filament voltage control so you can adjust the clipping level?Just separate the 9V for the chippy stuff from the heaters, rig two supplies. Replace the heater regulation with a buffered potentiometer.

This may "go too far", the lowest half or third of knob-turn may not do much. Or maybe it will. try it.