Hi tesla..
RSTheremins fix is really worth trying - If the problem is caused by harmonics on the pitch antenna (produced by the pitch oscillator syncing, or partially syncing to the reference oscillator) then a ferrite should attenuate these substantially.
I have been playing with some of my oscillator prototype boards since my last posting, and have certainly confirmed that there is a huge increase in harmonics at near-lock, and (surprisingly) even in full-lock... Both 2nd and 3rd harmonic levels are high enough that, when mixed with another oscillator (to simulate the volume oscillator) running at twice or 3x (+ a few kHz) the pitch oscillator harmonics + the 'volume' oscillator fundamental do mix (heterodyne) in the mixer to produce audio..
Must jst say that my real oscillators do not do this - My experiments were done on old prototypes with variable capacitors replacing antennas, so I could easily tune for worst case results.
It should also be possible to get rid of the problem by re-tuning either your volume oscillator (and its resonant tank) or by re-tuning your pitch and reference oscillators.. These should be tuned so that the frequency of the volume oscillator, when open, is far enough away from any reasonable harmonic from the pitch / reference oscillator.. But you will need accurate test gear, and a calculator, to set this up correctly.
Good Luck! ;)