"put a damper on human migration". Sorry, that won't do any good in this world--if there is large economic--or other-- incentive to migrate, humans will migrate.

A much better, and more practical, approach, would be to try to educate the poor--since with education comes a realization of the advantages of smaller families. It has certainly been so in the waves of migration to the US---which is the issue at hand.

And to try to get them climbing the economic ladder--to avoid being a drain on financial resources--since that seems to be a main objection of the restrictionists--at least the rational ones--the ones not yelling about "blatant, public treason".