There will always be sinkies.
Open the border, offer housing and jobs, create pink plastic cards for incoming people from everywhere else.
Don't even need to wait the conventional 9 months to create one!
This little island is essentially a hub for work and business. The economic model is molded in a way that the origin of a warm body on this land would not matter. As long as you've got brains and can work.
Of course, there's still the short and medium term policies to make the place hospitable for natives, i.e. placate the voters. That's just one of the inconveniences for the folks in politics.