Fuck me sideways a centre ground rationalist! I thoroughly enjoyed this article - I liked the balance and I like the way you've put the whole thing together.
Like you, I don't think there's an easy fix for this one. I think it has to be science led and on a sports by sports basis. I agree that when a sport brings in a myriad of advantages and disadvantages there should be a mixing of the sexes - and likely around the weight divisions and/or general build. Trans-people should be able to compete without any issues.
I think your idea of averaging is interesting too.... I would like to see men racing with women with the average advantages removed. I think that might be interesting.
Say for example the 100m sprint.... the cis-women go on whistle one, the trans-athletes on whistle two and the cis-men on whistle three. What you should then see is a fair race with an exciting finish, albeit somewhat unusual in its start. Those times could be refined and averaged - there would probably be an algorithm in there somewhere. :o)
Nailed it. Problem solved.