I'm now thinking the issue may also be the breadboards. Even though I'm only using rows with at least one row between them, I figure it may be causing some stray capacitances. Just want some confirmation before I solder everything onto protoboards. Has this happened to anyone else?
I assume you’re well on your way to getting a test theremin up and running.
Regarding your questions:
The room looks like a training lab; I’d be happy if that’s the case and if the students in your project learn more about the theremin.
If the tabletop isn’t metal but made of plastic or wood, everything should work fine. Also electric installations should not be near the antenas. Using a breadboard at this stage and at these frequencies is possible, and often even makes sense.
The problem is most likely the variable-pitch oscillator, and if I’m seeing this correctly, the 40 mH extension coil must have - separated and before implementation measured - a significantly higher self frequency than the pitch oscillator. That also means that the Q-factor of this coil must be either high enough, or you need a series connection of several 10 mH coils with high Q-factors as shown in the diagram.
Regarding the function: The function of the extension coil can be tested as follows: put a small capacitor of approximately 20-30 pF at the end of the coil and connect it to ground. Using a high-impedance probe on the oscilloscope (10:1), measure the resonant circuit voltage across this relative to ground. It should be in the range of several tens of volts peak-to-peak.
Without the participation auf the LC serial circuit, the range of the freuquency remains low.
Good luck for the next steps with your nice project!