> If our demographics start to diverge, we re-eval our process to look for bias or see if we can do better at recruiting
These are not good assumptions. 80% of pediatricians are women. Why would a hospital expect to hire 50% male pediatricians when only 20% of pediatricians are men? If you saw a hospital that had 50% male pediatricians, that means they're hiring male pediatricians at 4x the rate of women. That's pretty strong evidence that female candidates aren't being given equal employment opportunity.
A past company of mine had practices similar to yours. The way it achieved gender diversity representative of the general population in engineering roles (which were only ~20% women in the field) was by advancing women to interviews at rates much higher than men. The hiring committee didn't see candidates' demographics so this went unknown for quite some time. But the recruiters choosing which candidates to advance to interviewing did, and they used tools like census data on the gender distribution of names to ensure the desired distribution of candidates were interviewed. When the recruiters onboarding docs detailing all those demographic tools were leaked it caused a big kerfuffle, and demands for more transparency in the hiring pipeline.
I'd be very interested in what the demographic distribution of your applicants are, and how they compare against the candidates advanced to interviews.