But... no. Hard no to this. I mean, philosophically, I believe it's fundamentally wrong to tell people how they should experience their gender and whether they should be in "another" gender category because of the physical characteristics of their genitalia at birth. Trans women ARE "real" women.
On your first point, even if you are going to make this about brain chemistry, there is a robust volume of scientific literature that shows that gender dysphoria is caused by a biological mismatch between brain chemistry and outer traits of biological sex at birth. In other words, trans women experience gender dysphoria prior to transitioning because their brain chemistry more closely resembles that of women that are born with female sexual organs. So if you want to make this about brain chemistry, then you are fighting against your own point.
As for the point of whether or not trans people experience life as "real women," how do you know that every woman you come across was born with female genitalia? How do random strangers on the street perceive them? In many cases, especially when women are far enough along in their transitioning process, they appear to have been born female in their superficial sexual traits. And women who are mid-transition who are still exhibiting outer traits of maleness are subjected to constant sexual harassment as well. If anything, I think that many trans women experience a more severe form of sexual harassment than cisgendered women.
lol