It is hard to believe that there is no reward seats on the couple dozen of B1900 that come to NAS from South Florida every day. But I guess it is CO after all.
Have you checked with routings on DL or NW?
Have you considered JetBlue or Delta for paid tickets.
Delta is selling JFK-NAS tickets for July for just over $220 all in, hardly seems worth all those miles, even for six people. Prices are this low for July, because it is the off season, as the temps and esp the humidity are unbearable down here.