For a quarter of a century, the National Foundation for Advancement in the Arts has toiled quietly away in Miami, encouraging and supporting young performers, writers, and artists to the tune of more than $500,000 per year in grants alone. Now, the NFAA is making a stab at true national recognition, mounting a star-studded gala in New York and a continuing push for attention, all designed to secure the organization’s long-term future and make it a household name among arts types.