Patrilineal Jew

OK, I know the Orthodox and Conservative movements do not accept me as a Jew, and consider me non-Jewish. However, I would like to say that my father is Jewish through his mother, her mother and so on. I was raised completely by my father and his mother, never knowing my mother or her family. She is not Jewish, I know that. I was born as an accident when they were teenagers, and she left when I was very young. As I was raised by a completely Jewish family, raised as a Jew celebrating the holidays, learning the culture and religion, I can’t help but feel a great sadness overwhelm me whenever I think about the fact that I am not fully accepted by the people who share the same heritage and culture as me. It makes me feel a kind of existential anxiety quite often, and I often look up and read the same articles and posts about this. However, I can’t help but feel that my case is different, if only slightly, since I don’t even know my mother’s family. I guess this post is more of a comment than a question, because I already think I know what most of the answers will be. But let me try to pose this as a question. What advice can you give me? What should I do? How should I go about navigating this?