Which brings me to my conundrum. Is it wrong to identify with a label if there is no way of achieving it? Like if there is no surgical possibility of transitioning to the body that I want, am I still trans?
I can not say this loudly enough, but fuck yes you are!
You don't have to use the label if it doesn't feel right for you, but if it does, it's yours for the taking. Being trans is about who you are, not what you do. Being trans or gender diverse is about saying "This whole sex and gender thing you've assigned me, yeah, it's not working for me". And that's you. What you do with your experiences is up to you, but the experiences are there and they're real, no matter what your external circumstances.