[i]"You could try playing inside faraday cages. Or put an earthed (grounded) kitchen foil screen between you. That might work."[/i]
A grounded foil screen will work, but will add a huge increase in background capacitance, reducing sensitivity and probably requiring re-tuning of the instruments..
[i]"(Us "old" ones are too set in our ways to take on such a project :) )"[/i]
LOL! - Perhaps some of us "old ones" are still foolish enough to embark on such a venture! ;)
Sorry - What follows is probably only of interest to those with good [b]TECHNICAL[/b] / [b] ELECTRONICS[/b] knowledge..
A way which WILL** work (the basis of my directional antennas) is to connect the input of a high frequency DC amplifier to the antenna, and connect the output of this amplifier to the screen - the screen then tracks the waveform on the antenna, and is maintained at the potential seen by the antenna.. Because there is no potential difference between the antenna and the screen, there is no capacitive loading caused by the screen.. any 'outside' signals or capacitances hitting the low impedence screen are blocked. If multiple Theremins employ this scheme, with their independent screens blocking each others fields, one should be able to entirely block interactions.
[i]*This method is similar to the guard ring employed in sample/hold circuits, where the output of the amplifier is taken to a 'ring' on the PCB which goes 'round the holding capacitor.. the principle is identical - if the amplifier is exactly unity gain, then the voltage on the input cannot leak away, as its leakage path is obstructed by a low impedence 'barrier' maintained at the same voltage as the input voltage.[/i]
Practical problems..
Voltages on antennas can be high (easily 50V P-P) and impedence high, so the amplifier connected to the antenna needs to be quite special - it must not load the antenna, it must track the voltage on the antenna closely, and it must be able to output the voltage range on the antenna.
**I have not played with screening theremins from each other in this way, but have achieved directional antenna screening using this method. It is far easier to implement this when using low voltage antenna circuits (inductorless - RC type oscillators or 'digital' capacitance sensing circuits) but much more difficult if one is interfacing to conventional LC theremin circuits.. On my original PSoC designs, I was able to shape the sensing field using this method.. But the range was too short.. The complexity and expense of applying this scheme to higher voltage 'conventional' Theremin circuits has caused me to put this development in the 'do later' box.