Thank Dewster for your efforts. Lets make the sim better!
But there is still (IMO) a fundamental issue in your simulating. That is the coil's self capacitance. I know you used the David Knight' formula (5.3). And you didnt beer in mind that the formula corresponds the hypotetical case of "isolated" (or "flying") coil.
But coils in theremins are never "flying". For example, the EQ coil is a "grounded on the one side" (or "powered from the low impedance source", in pacticy).
According the LTL (long transmition line) theory of coil's self capacitance we have the 1/4 resonance system instead of 1/2 resonance. The different mode means the different resonace frequency and the different self capacitance value, as result.