Hello,

Have a look at the following schematic:

This comes from this page for the Minimum Theremin:
http://www.theremin.us/101/101.html

Bertus

 

This should work in theory. In practice the two oscillators may lock in sync for the reasons Mike gave in post #3.
The odd value for C2 models a 10pF cap plus coupled capacitance from a hand near the pad. Mixing is done simply by U3. R2/C3 filter out the high oscillator frequency (~100kHz here). The output is at the beat frequency of the two oscillators.

 

@tubeguy, i posted my schematic in post 1. The only change is my pulldown became a pullup resistor. I also added decoupling caps.

 

Sorry, after I re-read the entire post I see that I missed a few things.