AETHERPHON, global theremin family

>I think it would be very interesting to see a 3D plot of the capacitance 
   >field of the theremin, with those tuning setting superimposed on it.

That would be a big project.  Lots of data points to collect, and rather difficult.

The first thing, is to discard the idea that the "antennas" are acting as antennas.  They are capacitor plates. At these low frequencies they aren't anywhere near long enough, and the fact that diameter is as important as length confirms this.  

  I 
   >envision the field to be like a big cylinder, but I would assume the 
   >field is rounded on both ends?  Or is fatter around?
   >

Take a sphere, and stretch it a bit, and that's roughly right.