Commas are not grammar. They do not even exist in spoken English. They are conventional devices to clarify the meaning of written English, which does not benefit from tone of voice, stress, gestures, etc. Nor are the conventional devices uniform; the conventions mandated or recommended by different style guides have some differences.
With that said, I am not sure that your first two examples are valid.
X has a daughter, who is a doctor.
does not necessarily imply that X has only one daughter.
X has a daughter, who is a doctor, a son, who is a dentist, and another daughter, who is a lawyer.
The preceding example strikes me as being a perfectly acceptable sentence with standard use of commas. Do you believe that it is meaningless because it is ungrammatical, that the first descriptive clause entails X has but one daughter and so logically is inconsistent with the end of the sentence?
X has a daughter who is a doctor
does not necessarily imply that X has multiple daughters of which only one is a doctor.
X has a daughter who is a doctor. She told me I needed to go to the hospital immediately.
The thrust of that paragraph is that it was a doctor who warned me to go to the hospital, not some random person.
You are taking too literally the terms "restrictive" and "non-restrictive" clauses. It would be better were they described as "essential" and "incidental." In speech, an incidental clause is marked by a pause before and after it whereas an essential clause is not preceded by a pause. Comma usage in this case mirrors the pace of spoken English. (I do not mean to imply that all the conventions of punctuation in written English correspond to pauses in spoken English.)
Let's go back to the sentence you are asking about.
This is a new situation for me
makes perfect sense on its own (on the assumption that the referent of "this" is understood). The phrase "being ..." is incidental. So you are correct that standard punctuation calls for it being preceded by a comma. If you say it aloud, you are quite likely to leave a short pause between "me" and "being."
I suspect that thinking in terms of essential and incidental will make more sense than assuming that rules of punctuation sound in set theory.
