Yes! Yes! All that!
And my native language (French) doesn't have a neutral grammatical gender, but then I learned some Dutch and German, as well as English with its "it" pronouns, which all made me really comfortable with the concept of separating actual gender, sex, and pronouns and grammatical gender. I know the use of it/its pronouns for a person, like you mentioned, is really touchy and loaded in English, but I jumped to claim it the minute I realised I was nonbinary (on top of also using they/them and she/her), because this feeling of being completely divorced from any gender at all, even grammatical. It gives me the same gender euphoria that Beth described above. Especially since it is impossible for me to get that in my native language.
In French, I can be a she the same way that Beth is a she (deliberate, conscious, that's our gender), or the same way that a table is a she. And in English, I can be a they the same way that a stranger with an unknown or irrelevant gender is a they, or I can be an it, the same way that a table is an it.
Genderrrrrrrrrrrrr