Sounds like you are making progress.
One symptom of a grounding issue is when you touch a metal component on your Theremin the pitch jumps. In this case, the Theremin and/or your sound system isn't connected to a good, earth ground. A possible work-around to this situation is to use a conductive wrist strap with a cord and alligator clip. Put the strap on your wrist and attach the alligator clip to a ground point on your Theremin.
A wrist strap probably won't solve a ground-loop situation, though. The solution is to reconfigure all your equipment to eliminate ground loops (which can be a bit of a chore). The other is to use a device, such as the Ebtech Hum eliminator to isolate the Theremin's ground from the rest of your equipment and then use the wrist strap to ground your Theremin to yourself.
Now, if you still can't get rid of the distortion, then there is a source of electrical interference in your area. The way you can locate this is to set your Theremin's pitch control to produce a continuous pitch. Then, while listening to the Theremin, start turning off lights, computer equipment, etc... one at a time. If you turn off something, and the distortion stops, then you have located the problem.
In my studio, one of my external scsi drives was a culprit. Since I don't need to run it most of the time, I just keep it turned off to keep my Theremins "happy".
If you can't eliminate the distortion by turning equipment off, then try playing your Theremin elsewhere to see if the distortion changes or goes away. Try other rooms in your house, or even try it at a friend's house.
I would suggest to just "hang in there"... indeed, I have dealt with all the above problems at one time or another. Some patience and experimentation will lead you to a solution.
Best wishes!