Tokyo Godfathers/Headscratchers

Okay, I've watched the movie through, and I'm still not sure. Was Hana supposed to be a Camp Gay crossdresser, or a Transsexual? It feels like the writers either couldn't decide, or didn't know there was actually a difference.
 * I think she is a Transsexual. She seems to identify with being a woman, as opposed to merely liking to dress in women clothes, so she is not just a crossdresser.
 * Hana even says something like "God made a mistake with me, in my heart I am a woman".
 * No, crossdresser. When they go the hospital, the doctor refers to Hana as "he" in conversation with Gin. Since he's giving advice on what Hana should do, he must have examined Hana before this conversation. Ergo, he knows Hana is physically male. Also, Hana uses the self-descriptions "homo" and "queer" several times. If Hana were a transsexual, she would identify herself as a heterosexual woman and wouldn't use those terms. (We know Hana prefers men because, as Miyuki notices, he loves Gin.) In the original Japanese, Hana uses the self-descripton "okama", which is a slang term for a homosexual male, especially a crossdresser.
 * Hana's physical gender has absolutely nothing to do with it. It's not like she could afford an opperation if she wanted one. Hana explicitly states that she’s a woman in her heart, and says that she always fantasized about being a mother with a husband. One of the implied reasons she’s so obsessed with motherhood and taking care of Kiyoko is that it’s a way she can be a woman; she can’t retroactively make it so she was born female, she can’t make it so people see her as a woman, but she can take care of a child. When Hana’s being melodramatic and talking about what she wants and how she wants to be seen, she uses feminine language. When’s she’s feeling down about herself or is referring to the way people see her, she uses masculine language. This alone is enough to qualify her as transgender.