"can it be that the grounding via audio cable is not as good for the theremins performance as another option to ground the machine?" - Flub
Yes, IMO it can be.. As in, its always IMO best to have independent centralised grounding for all audio equipment.. But this is a complete subject on its own.
Back in the days of real Hi-Fi, all quality seperates had a ground terminal for this purpose..
These days one needs to hack a ground connection by having a ground wire coming from the audio plug - Chop off the moulded mains plug on your PSU and replace this with a plug where one has access to the ground connection, then run the ground lead to this..
Or, If you know what you are doing (or if you have a wall wart and cannot chop then plug off) , get a quality extention strip, open it up and insert some banana sockets into it wired to the ground bus... You can then plug banana plugs into this ground bus.. Or you can go straigt to the mains plug and carefully add a ground wire here..
Warning! - If you are not absolutely sure you know what you are doing.. As in, ABSOLUTELY - There is no question, and you understand every word fully and know this will be easy for you and you have no possibility of making an error.. Dont mess with mains!! If you wire it up wrong, if you connect Live or even Neutral to your ground output, it could do damage and could even be fatal!
If setting up a "studio", I would get inside all the equipment and put banana sockets in them connected to their ground, and this way have pluggable leads to facilitate grounding ..
But its a lot of effort - For the theremin, I believe the effort is worth while - For most other gear, possibly not.
Fred.