Affluence is indeed a big factor in the equation, in that as a rule, the greater the affluence of individuals in a society, the fewer children they have (utility maximization). So a plan to increase the general affluence of all the world’s people will help. The approaching “zero marginal cost” economy will have a major impact by redefining “affluent” — when everything is free or nearly free, who is affluent and who is poor? — but it remains to be seen whether the current economy’s 1% will allow that revolution to take place at all, let alone share the new affluence with the 99%.
My personal opinion (note the “SciFi Scribbler” in my profile) is that the pressure to solve the sustainability problem will be the fuel that takes Humanity to the stars. The real problem is not how we eat. It is that, in the present moment of history, our brilliant and beautiful species, with an unlimited potential for growth, is pushing against the artificial limit of confinement to a single, small planet. I see our confinement, rather than our growth, as the problem.