Yes, we are somewhat different than cisgender women, but we are still women as much as they are, and that is my point. We deserve to be treated like women in every way unless there is some insurmountable logistical issue that prevents this, which is rare.
It is not just semantics, it is the heart of the matter.
But if the treatment is the same despite the different terminology?
Which is the core? the terminology or the treatment? Because You can be referred to with different terms but treated the same or be given the same term but treated differently.
If you want people to agree that you are women as much as they are, you have to have a definition where that is true. Right now, you are working with one definition while others are working with another. The definition they are working with was not created to alienated trans-women, it's the historical definition. You are proposing changing that definition to something more inclusive. If you are going to convince people to adopt something closer to your definition they need to know what that definition is.
Even some of your allies, such as LondonJohn have rejected self-ID as a definition because it's not a definition. You say you feel like a woman. And I believe you. But what does a woman feel like that you can objectively compared?
If someone's father passes away, I can say "I know how you feel" but that's inaccurate. I know how I felt when my father passed away and assume that that person feels similarly. The way you feel is how you believe a woman feels, but it's not testable.
For that matter, I don't even know if the way I feel as a man is the same as how LondonJohn feels as a man.