In your opinion, does
my definition invoke subjective personal identity?
No, but it substitutes a subjective societal identity, and it's equally circular.
The other definition: A person is a woman if she identifies as a women.
Your definition: A person is a woman if she acts the way society expects women to act.
Or "is expected" to act the way society expects women to act. So in your definition, a person is a woman if they are expected to behave in a feminine manner, with "feminine" being defined as the way society expects women to behave.
So, that person with the penis over there is expected to watch a lot of football on Sunday afternoons, but instead they sit glued to the Hallmark Channel. Does your definition help determine if they are a woman or not?
ETA: Let me get it as close to your precise wording as I can.
A woman is a person who is expected to behave in conformance with the cultural expectations of humans born with ova.
I'm not seeing how that works for classification. At least, not unless all people born with ova are expected by society to behave in a certain way, in which case all people born with ova are women. That definition works for me, but I would prefer to eliminate the behavioral expectations.