We have exactly that problem in Florida. The Southeast corner of the state is full of ex-New Yorkers who are trying to do for Florida what they did for New York. One of the state's more popular bumper stickers is "If You Love NY - Take I-95 North"
There is a huge difference between the NYers moving to NC and moving to Fl. The ones moving the NC are young to middle age, working, starting businesses, building their careers, starting families, etc...
The ones moving to Florida are going there because it is God's Waiting Room and are of the "I'm old, gimmie gimmie gimmie" mindset.