I don't think we can avoid adjustable inductors due to variable component tolerances, but they are available from digikey and are cheap. Adjustable capacitors should not be needed. Diodes or transistors can and do serve this purpose. The EW uses transistors as electrically controlled capacitors to fine tune the pitch and volume oscillators.
For pitch tuning, the EW adjusts the reference oscillator, and this is not the best place to do this. Fred's idea tunes the antenna circuit, which is better.
Keeping adjustments to a minimum has always been preferable.
The important adjustments are setting the pitch and volume oscillators to the resonant frequency of their antennas and can be done with an RF probe and volt meter. Very easy to build and use.
One of the goals of this project is learning how a heterodyning instrument works. I think documentation is at least as important as circuit design. If the builder understands how the antenna circuit interacts with the oscillator, tuning will be much more intuitive.
High gain in an oscillator is both a blessing and a curse. The currents in a resonant circuit are much higher than in the bits driving it. This can lead to instability due to component heating surprisingly fast, even in low powered circuits. The goal is just enough gain for reliable operation.
Uncle Bob's EW oscillator has a lot going for it, but obviously we don't want to rip it off. There are plenty of other proven designs, although I think it would be best to avoid taped inductors.
Higher frequency's do require smaller linearizing inductors. There are compromises. The linearizing inductor forms a series resonant circuit with the antenna and hand capacitance. As we move up in frequency, the inductance needed goes down, but the antenna capacitance says the same, therefore the pitch range goes up because the ratio between L and C is greater.
Higher frequency = more octaves.
If we go too high, we run into the AM broadcast band. A theremin operating on the same frequency as a 10,000 watt transmitter would not be a happy thing.
I don't think we can eliminate linearizing inductors. To be playable a series resonant antenna circuit is needed.