<rolls up sleeves>
Did I mention that your usage of the word "precision" is rather lax? As was drummed into me at college when I was studying computers, Precision and Accuracy are two different things...
If I were to say that the ratio of a circle's circumference to its diameter was 27.6384849294756 It would be quite precise but very inaccurate.
If I were to say that it is about three and a seventh I would be quite accurate but very imprecise.
(If I wanted to show off I would mention that as an approximation 355/113 is both more accurate and surprisingly precise.)
It is in the nature of the theremin that absolute pitch precision is impossible - we just can't stand still enough to maintain an invariant pitch, or home in on a particular frequency faster than the ear can hear or more accurately than the ear can discriminate - but your recordings (to give a sycophantic example) are among the most accurate that I have encountered.
As for reproduction, this is only a matter of degree. No two performances of any classical piece on any instrument played by a human are the same - there is plenty of scope for interpretation between the score and the rendition. If this were not the case then we would not have the opportunity to prefer one performance of the piece over another.
All my performances of a particular piece that is in some part aleatoric are also different from one another - more so than your classical performances, but they are all still recognisably performances of the same piece - just as no two oak trees are the same, but they are all oak trees nonetheless.
If you want to hear exactly the same piece twice, it has recently (in the last couple of centuries) become possible to capture the sound of a performance and cause it to be reproduced at a later time. This was not the case when classical music was established as a form and probably goes some way to explain the preoccupation of the classical musician with exact reproduction of a piece.