"The 3 pi RF choke is a thing of the past." - BBrinkman
Indeed. RF chokes, like virtually all commercial inductors, are the way they are mainly due to miniaturization pressures, the results of which run counter to Theremin use. So you are stuck with hard-to-find old-school oddities that sort-of work when pressed into a service they really weren't designed for, or you wind your own.
The winding pattern would be difficult to home-brew, but there's nothing magical to the way they operate. If your aim is to make the best Theremin coils, you start with the least temperature sensitive core (air or some formulation of ferrite) and get the self-capacitance for your target operating frequency within an acceptable range. Correcting for temperature sensitivity is difficult to do with tempco caps and the like, it's best to nip it in the bud at the source.
Theremin EQ coils don't have to conduct any significant current, so wire gauge isn't critical. You can pick the finest wire you can easily work with and it probably won't negatively impact Q much.