There is a much simpler way to get to a steady-state economy. All economic activity, with all of its effects on the environment, leads to consumption, i.e., the acquistion of goods/services by people. Consumption depends on personal income. Fix personal income, and the only variable is population. Experience has shown that people with a stable income sufficient for one to three children will have on average two children--the number needed for a stable populaton.

If curious, a paradigm for establishing a stable (bulletproof, actually), sufficient income (without any distopian authoritarianism) is in "To Preserve What We have, What We Have Must Be Enough" (here in Medium, but not behind the paywall).