"You don't need another mixer. If the fixed oscillator remains at 440kHz while the variable one goes down to 420kHz, the beat frequency will be 20kHz which is almost inaudibly high and will be damped by the low pass filter in the mixer. You will have to re-tune the fixed oscillator with the variable capacitor down to ~420kHz, too, to get an audible beat frequency. The active mixer acts at the same time as a 100Hz high pass filter, a 3kHz low pass filter and amplifier. Thus, as soon the beat frequency will be within the 100Hz to 3kHz range, you should get an audio signal at the output. You can also try to trim both oscillators temporarily for a 1kHz beat frequency without connecting an antenna (i.e. 440kHz and 439kHz) and then check the signals at the gate, source and drain pins of the mixer get with an oscilloscope, and post pictures here. I'm sure that we'll get it up and running."
Sorry for the late reply. Last Friday, we were finishing our autonomous quadcopter project that we built from scratch. We wanted to use theremins as human proximity capacitive sensors so it would follow humans around while making sound, but could not get a decent range with our RC oscillators. Basically, the output of the theremin is sent to a high pass filter, and only when the theremin outputs at the cutoff frequency (human at a certain distance) will the microcontroller detect amplitude over a threshold.
Below is the pitch-only Thierrymin I breadboarded hastily, the top being the voltage regulator and mixer, and the bottom the fixed and then variable oscillator (with the trimmer cap and antenna removed temporarily):
The capacitor that connects the speaker with the mixer above is placed incorrectly. But after correcting it, we still could not get output from the mixer. The oscilloscope should have read even an ultrasonic output, but each of the JFET pins is not outputting anything.
We simply used a simple RC oscillator in our project, and I just want to finish this Thierrymin to give as a Christmas gift!
EDIT: When we showed our TA your oscillators he was really impressed.
EDIT2: Oops, I forgot to say that the 8k2 resistor in the mixer in the picture was misplaced--it was connected to G instead of S. We corrected it, but still no output.