You should have followed the technical evolution which Moog did for the Etherwave Theremin (the commercial version of the EM-Theremin). Already a long time before switching from the TOKO inductors to the COILCRAFT inductors, they replaced the variable 100u inductors in the pitch oscillators by a combination of a fixed 47uH and a variable 47uH inductor in series. Similar in the volume oscillator: the variable 68uH inductor was replaced by a series combination of a fixed 22uH and a variable 47uH inductor.
When Moog switched from TOKO to Coilcraft, they additionally modified some resistor values in the oscillators for adapted impedance matching and stability:
R15, R19 from 470 to 330 Ohm
R2, R6, R16 from 2.2K to 1.5kOhm
In ever case, it is normal that good RF inductors have a DC resistance near 0 Ohms which does not have a negative impact on a well designed RF circuit.
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But all that has nothing to do with the voltages across R23/R24. These form a voltage divider and a low pass filter together with C23. Thus it is somewhat useless to measure the frequencies across these resistors. Since D4 acts as a mixer/detector diode, the signal across it (and thus across R24 and R23) depends strongly on the frequencies and amplitudes of both pitch oscillators. If the difference of their frequencies is > 7kHz, you'll find naturally almost no signal across R24. First you need a deep understanding of the principle of operation of a theremin in general and then of the function of every single element of the EM circuit.
Your question about the 68uH inductor makes me think that you didn't yet understand the principle of operation of the three differential pair push-pull oscillators in that circuit. It is idiotic to try to build a circuit without understanding what every circuit stage does and how it does it.
Then, you need an oscilloscope and a frequency counter.
All that is somewhat tricky since the pitch antenna will react to everything around (including the oscilloscope and the frequency counter). You might disconnect the antenna and replace it temporarily by a fixed 10pF capacitor towards ground for a first testing and adjustment of the variable inductors.
a) Make sure that the fixed pitch oscillator is correctly working: 24Vpp centered around +12V at the collector of Q3 with the oscilloscope and 287kHz at the base of Q4 with the frequency counter.
Now it's a good moment to check the operation of the pitch tuning potentiometer P1: Moving it from its center position to the right and left extreme positions should vary the frequency of the fixed pitch oscillator from 286.6 to 287.4kHz.
b) Make sure that the variable pitch oscillator is correctly working: 24Vpp centered around +12V at the collector of Q1 with the oscilloscope and 286kHz at the base of Q2 with the frequency counter.
It is important to disconnect the oscilloscope while measuring the frequencies because the additional capacitance of the oscilloscope probe will de-tune the oscillators.
When you are sure that both oscillators produce the correct amplitudes AND frequencies in a stable and reproducible way, then and only then you should find the aforementioned 1kHz signal (0.6Vpp) across R24 which will look like a two-way rectified sine wave with the "peaks" at 0V and the "valleys" at -0.6V.
Obtaining that signal proves the correct operation of the pitch circuit.
If you are done, please post back here and we can move over to the volume circuit.