I'm not sure I understand what you're saying. What does gender have to do with population density? I chose population density, because it was the only value that I could think of that closely correlated with culture and that was not a protected status (ie, not race, religion, sex, etc). If it's done algorithmically, it doesn't seem like a bad measure.
Anyhow, the "who gets to choose" thing is tough. Right now legislators get to choose, but the judges said that they are failing at that, so IIRC, now an academic from a state university got to make some map adjustment. Ideally, I'd have a committee of academics provide vetted map recommendations that elected officials choose from, and that a judge signs off on.
My interpretation was that you chose to group together areas with similar population density because there are important policy concerns directly related to population density. And indeed that's true: water rights, zoning, building codes, pollution and noise restrictions, and more ought to depend highly on the population density of the area, and it doesn't seem necessary or even moral for rural voters to have much say in how dense cities set those policies.
But my point is that there are plenty of other policies which don't (or shouldn't) vary based on population density, and thus grouping districts based only on population density might give very little influence to interest groups for those other policies. Civil rights are the extremely obvious example, but there are others.
What you’re probably looking for is an increase in the number of Representatives rather than a change in the formula of districting. I am at least.
Look at it this way, if it were 1 Rep per between 30K and 50K instead of 1 Rep per ~700K, there is a decent shot that somewhere in those several thousand Representatives you’ll have a few that are from just about every slice of American life, and elections are still every 2 years if one session of Congress just isn’t good enough for you. Even Wyoming would be sending between 12 and 19 Representatives to Congress rather than the lone Rep they send now, and would have more and various opinions and interests represented.
Anyhow, the "who gets to choose" thing is tough. Right now legislators get to choose, but the judges said that they are failing at that, so IIRC, now an academic from a state university got to make some map adjustment. Ideally, I'd have a committee of academics provide vetted map recommendations that elected officials choose from, and that a judge signs off on.