What makes you think trans women do not experience misogyny? Do you really think the patriarchy sees trans women and says, “you get a pass because you were assigned male at birth?” In fact, the opposite is true. Trans women are treated differently by society, even before they transition. You may not realize this, but it is a form of misogyny whenver nascent trans women are called “Fa___t,” or “sissy.” Whenever a trans woman is beaten up or killed, just for being trans (or just not fitting some guy’s idea of what we should look or act like), that is misogyny. And what about kids who transition at a young age: does a five year old trans girl not experience misogyny? You can bet she does.
And yes, most of us trans women would gladly experience whatever it means to be a woman if we could, even including a heavy dose of misogyny and discrimination (more than most of us experience even now) if it meant others acknowledging that we are women. As it is, it is only a matter of degrees: all women — trans or cis — experience misogyny. Unfortunately, some of us also experience discrimination from other women as well.