"My question is - is the internal tuning process something that will help with linearity, or does that only affect pitch range and distance?" - kc5string
Thierry can probably answer this better than anyone, but my $0.02 is this:
There are three LC resonances to deal with on the EW pitch side. The first is obviously the LC tank of fixed oscillator that beats against the variable oscillator. The second is the LC tank of the variable oscillator. The third is the LC formed by the series inductor L and the antenna / hand capacitance C.
The variable inductor for the fixed oscillator gives you coarse control over the first resonance, and the pitch knob on the front of the EW gives you fine control here. The variable inductor for the variable oscillator gives you coarse control over the second resonance. The wire connecting the PC board to the pitch antenna travels over a grounded piece of aluminum tape, and bending the wire up / down gives you some kind of control over the third resonance.
The trick is to get them all aligned in a way that maximizes perceived pitch linearity, particularly I believe near the antenna (but I could be wrong). Good luck! The EW is a tricky beast.
FredM's tuning approach was to tune via the third resonance by saturating the series inductor, and I believe Theremin's approach was to also tune via the third resonance, but with an explicit variable capacitor. Moog's tuning approach is clearly to tune via the first resonance, which is sub-optimal IMO. (My approach is to avoid this analog kludge altogether.)