"Moving the pitch hand down, parallel to the rod and over the enclosure, causes a significant rise in pitch." - Gordon.
I suspect this is more to do with the case being effectively the theremins ground, or capacitively coupled to the "0V" or "ground".. (in fact, I dont just "suspect" - I am sure of this)
One gets this effect with any and every theremin where the hand capacitively couples to the circuit (board) and to the antenna.. Particularly if the theremin is not well grounded and the primary coupling from the antenna to the theremins ground is via capacitive coupling directly to the board / case.
The case being conductive acts as a good capacitor to any "ground" in the theremin - "ground" is an illusion - The theremin requires that there is a capacitor between the antenna and its "return point" - you form part of this capacitor.. If the "return point" is connected to "real" ground, then you can close the capacitive connection by (capacitively) coupling to any ground.. But if connection of this "return point" to "real" ground is poor, then direct coupling to the "internal" "return point" can be significant, and will increase pitch compression closer to the antenna.
Linearity and range / sensitivity requires the best possible grounding / earthing of the theremin.. Any theremin!
Fred