Interesting topic! These are my personal thoughts ...
Actually, it's something I've given a fair amount of consideration to over the last year. When I first started to play, the same thought passed through my mind as yours, and I tried a few experiments.
When learning to play the theremin I soon came to the conclusion that tuning as consistently as possible was absolutely vital if you wanted to establish reasonably consistent aerial-fingering that the "muscle-memory" wouldn't forget! But I also soon realised that absolute consistency in tuning is virtually impossible.
One problem with you marking the theremin case with two reference points that, when your fingers are on them, give notes a fifth apart ... is that you don't play the theremin on its case. The same two fingers held the exact same distance apart at your regular playing height almost certainly won't be a fifth apart because the note field curves and notes are closer together nearer the top and bottom of the pitch field.
You can test this by holding your right hand about four inches from the bottom of the pitch antenna and moving it slowly upwards keeping exactly parallel with the antenna; the note will change a semitone or two or three between the top and bottom.
Another experiment is to start with your right hand at the bottom of the pitch antenna and move it slowly upwards while trying to stay on the exact same note. You'll find you have to gradually move your hand further away from the antenna. Go right up above the antenna, down the other side and under the bottom, (still keeping on the same note) and you'll roughly trace the shape of the theremin field, (which is somewhat egg-shaped or, at least, the route your hand takes will be like the drawn outline of an egg sliced exactly in half from top to bottom , (with the narrowest end of the egg pointing downwards).
Where it gets problematic is that if you do the same with another note (say an octave or a fifth higher), then another note another octave or fifth higher, you'll probably observe that the shape alters slightly with each repetition of the "outline", so that the curve in the centre area of the "egg" bulges out a little bit wider each time (with a non-linear theremin like the Etherwave Standard that is; the same experiment with the E-pro suggests a a note-field that's more like a straight-sided sausage ... although they're not precisely egg or sausage-shaped, that's just to illustrate).
Another interesting test is to move your hand in and out from your body (at exact rightangles over the theremin) but keeping it perfectly parallel to the antenna; again you'll hear the note change in keeping with the shape of the note-field.
Anyway ... imagine an invisible egg-shaped note-field. Now, think of each octave-worth of notes like an invisible egg within an invisible egg within and egg etc ... but with the smaller eggs getting narower and less egg-shaped rather than keeping in perfect proportion. Now imagine that sliced in half so you can see the "layers" of octaves ... and the octaves nearest to the bottom of the "egg" are a little more compressed than those in the middle.
That's why fingers a fifth apart on the theremin case aren't really a fifth apart in playing position.
I eventually came to the conclusion that using a practiced/established finger shift of either a fifth or an octave to tune a non-linear theremin worked best ... but only worked consistently if
A) you do the finger-shift at the same height above the theremin case every time (preferably at your regular playing height), and
B) Because the field is curved, even when your hand is always at the same height you must try to keep it the same distance in/or out over the theremin, (again, preferably at your usual playing position) ... and
C) That you always tune to the same note each time, (because the notes/octaves become more compressed closer to the pitch antenna ... so that a