How about an artificially anonymized process. HR does know, or assumes, your gender from receiving your CV. But from that point onward your identity is anonymous.

For instance, HR creates a throw away email which will be used during the hiring process to coordinate the rest of the tasks. The coding interviews could use one of the many platforms we have for shared/same space coding with an added chat box for talking your way through the problem so to say.

And so hiring decisions are done by interviewers without knowing the gender or how the candidate looks.

I think this would allow for a good level of blind testing, but would provide some downsides in the side of cultural fit screening. It's a lot easier to pretend you're not an asshole in asynchronous text-only communications.

I guess everything carries a trade off.