Okay, I'll bite:

0) I'm not sure it's best that anyone exist at all, but for the sake of a post let's assume they should.

1) Assuming the resources (which seem to be implied in the ability to change the gender ratio in the first place) nix men entirely. I'm probably more skeptical than the average LWer that traditionally male pathologies are inherent to my sex, but there's a decent chance I'm wrong about that, so there's that. More importantly this gives public institutions veto power over the creation of new people in a way that isn't bodily intrusive.

2) People own their bodies; the state owns the means of production, which are rented out by cooperatives. Investment decisions are guided by prediction markets. Public goods are provided by the state on a universalistic basis. (This is assuming we still have to deal with scarcity.)

3) Raising children is a compensated service to the state, in principle not separate from other forms of market production. (More tightly regulated, obviously.) Reiterating my caveat that I'm more of a constructionist than the typical LWer, eugenic opportunities present themselves, as do opportunities for speeding up the destruction of ascribed ethnic status.

4) Legislators chosen by sortition, either from the general public or some sort of ascetic public service corps.

5) If we have the resources, Destroy Nature (but keep public gardens large enough to hike in.) If we can't get rid of most other animal life, at least get rid of factory animal farming.

I don't think this would be fully stable (I don't think I could endorse anything that would) and I don't doubt it would horrify plenty of people, but if I could press a button this is what I'd press it for.