Okay, now I understand better

The example you provided is perfect for special 510(k). EMC testing is a well established method and often performed by a third party lab.
And, as you probably noticed, they give allowance to change the environment; not the intended user.
In essence, you are taking the decision making or treatment away from the healthcare professional and giving it over to the lay person.
FDA doesn't "swallow" such things easily.
With therapeutic devices, I've seen cases where the manufacturer developed a less powerful device for the home use.
With diagnostic devices, I've seen cases were the manufacturer changed the device and/or labelling to address concerns for misinterpretations.
I am all for shortcuts, but this is a tough one and even more so since you wrote that there is no predicate device approved for OTC.
Shimon