I can't, because of the conditions you set.
But this is why trans people claim GC people "erase" them (ridiculous term).
Transgender people clearly exist or there would be nothing to debate. But by setting rules like you have, it becomes impossible to define a trans person.
With no rules, my definition would be:
"A Transgender person is someone who has an internal sense of their sex (referred to as their gender identity), and that internal sense differs to their biological sex".
I have no issue with that definition, in the same way as I have no problem with other people describing themselves as Christian when I don't believe in God.
That definition would work for me as it suggests not everyone has a gender identity, people can just identify with their sex. And makes it clear there is a definition between someone's perception of themselves and biological reality.