Last weekend, the Metropolitan Opera broadcast its final live performance of the season, the last time the series will carry a sponsorship credit for Texaco, which kept the opera on the air for more than six decades. And while the Met has found money to cover the cost of next season’s broadcasts, the long-term future of the wildly expensive series is still very much in jeopardy. Met chairwoman Beverly Sills is spearheading the effort to solicit donations for future seasons, and her basic strategy is a simple appeal to the warm, gauzy memories of all the moneyed folks who grew up listening to the Met.