Sorry, I had forgotten that I did listen to your first clip. Your most recent clip has the theremin sounding like a kazoo. I agree that this isn't good.
The pitch response seems to be working, even if the sound is terrible. That's something, at least.
Since you believe this to be a result of the impact I think you may want to give it a very thorough internal visual and mechanical inspection. This includes tugging on connectors, maybe even removing and reinserting them to refresh connections or spot possible problems. Look for anything that could have suffered from the way it fell, knowing that anything with some mass is more likely to be damaged by a high-G impact.
The narrow CV board to which the potentiometers are soldered does contain the headphone amplifier IC but not much else in the audio path. Since the pots don't seem to be having much effect you will want to make sure that the connection from the CV board to the main board is good. Look at everything, but focus on the larger main board and the connections to antennas on both ends. These antenna connections won't affect tone, but a broken ferrite in one of the pi-wound inductors at the end could affect the response (most likely killing it though).
What are your options for sending the unit somewhere for repair? Did you buy it from a dealer that can direct you to a warranty facility (even though this may not be covered due to damage)? If warranty repair is out of the question then you could probably send it to Thierry Frenkel (France) who could not only fix it and tweak it to perfection but you could have him put in his ESPE01 buffer mod that will greatly improve the instrument's linearity and tone (for a fee, of course). Many Etherwave owners have that mod installed or something like it.
Judging by your video title I can see that you are a science/mathematics/engineering nerd (as several of us are as well). Do you have any test equipment (scope, DVM)?