... to prove what exactly? That humanity will inevitably overcome the issues which overpopulation begets? That our population will plateau before we reach 250 billion if we close the gender gap? I feel like your comment was really vague, and you answered jrs99's question somewhat obliquely. So I don't know what you're arguing. But if your Amazon link is anything to go by, I assume you predict a decrease in the world's population.
Also, I don't think we can continue to extrapolate history as you imply. I used to think that our age was no different than any other age. I used to think "Humans have always had the same needs, right? Technology simply gives us more effective ways to satisfy them. Technology changes, but Humanity's needs have stayed relatively consistent."
Randell Munroe's project "Time" changed my opinion. To roughly paraphrase, "Whatever civilization comes next won't have fossil fuels to jump-start another industrial revolution." And I began thinking "Huh... I guess that makes sense. Fossil Fuels make us pretty unique, doesn't it? There's a pretty low probability that we'll find an energy source more dense and convenient than Fossil Fuel. Things like solar and fission are certainly nice. But if they packed the punch that Fossil Fuels did, they'd have dominated our economy already! So does Fossil Fuel represent a limiting reagent (chemistry term) on what Humanity can achieve?"
I think you and the astrophysicist can agree that something has to give. And perhaps closing the gender gap will plateau the population before we reach 250 bil. But given this fails and the population reaches 250 bil and we live in dystopia anyways (like jrs99 originally asked), do you still believe that eugenics are inherently immoral?
[I'll take up that offer and start reading up on the famine.]