In the top of a double boiler, beat eggs and yolks. Stir in 1/2 cup of sugar, lime juice and peel. Cook over simmering water while gradually whisking in butter. Cook and stir until mixture is thickened and reaches 160 degrees. Strain; refrigerate until completely cool. In a mixing bowl, beat cream and vanilla until stiff peaks form; gradually beat in remaining sugar. Gently fold into lime mixture.
Split cake horizontally into three layers. Place bottom layer on a serving plate. Spread 2⁄3 cup lime mixture. Repeat. Place top layer on cake. Frost top and sides with remaining lime mixture. Sprinkle with coconut. Refrigerate for at least 30 minutes before slicing.