basic experiments

Oh yes, you need a lot of spare time to find that out, which I'm afraid neither of us have.. Is there a professor out there looking for a physical measurement internship for students, a thesis?

I have tried some simulations in LTSpice. Also time consuming, but the program does most of it autonomously. Here a first result. I analyzed the time signal of identical two mixed oscillators with a buffer to decouple them and vary the C (hand capacitance) of one. Coupling is made with k factor of the coils. Every point in the diagram is a single simulation and estimation of the beat frequency after demodulation. More points and values can be inserted next time.  

Without coupling you have the strong linear proportionality of hand capacitance to the pitch (math please find in this thread some pages before). The coupling compresses the pitch behavior compared to the hand capacitance and the pitch abruptly collapses to zero.

Don't confuse this with the linearity of the pitch in relation to the hand distance! The red and the green values gives better pitch linearity versus hand distance. .

"Coupling is made with k factor of the coils."  - JPascal

I'd imagine the coupling on something like the Etherwave, where it happens via capacitors going to a non-linear mixer, and the pick-off point is between the tank an the EQ coils for the variable pitch oscillator, must be a rather complex thing?  Still definitely worth pursuing this, and simulation is likely the best initial route!