Others have addressed some of your other points, but
would you mind inventing a new word either for gender-neutral third-person singular pronoun, or one for what “they” mean to foreign English speakers
We actually have that. Xe / Xem / Xyrs. It isn’t very widely used though, and is generally considered a neo pronoun.
Honestly I don’t really expect it to get mainstream use anytime soon, in part because people are already accused to the singular They / Them / Theirs (except for when a nonbinary person asks to be refered to as such).
Others have addressed some of your other points, but
We actually have that. Xe / Xem / Xyrs. It isn’t very widely used though, and is generally considered a neo pronoun.
Honestly I don’t really expect it to get mainstream use anytime soon, in part because people are already accused to the singular They / Them / Theirs (except for when a nonbinary person asks to be refered to as such).
There’s more than one option, I for one prefer Elverson which is Ey/Em/Eirs