women are not allowed to be successful on the same terms as men.

Right, because current Olympic sports are almost exclusively ones where having a male body gives you an advantage.

Imagine someone invented a new sport where women had a natural advantage. Say, some kind of obstacle course where a small body size and flexibility was the most important thing. I can guarantee that if a group of men competed in that and one of the competitors won because he had a very feminine body, people would question whether he was really a man.

So for what you’re proposing to work, the criteria must be simple, wide-reaching, and unassailable

And, I don’t think that’s possible. Sex and gender are simply too complicated. There will always be some arbitrary line that a lot of people think is unfair, and that disadvantages people who happen to fall on the wrong side of it.