Combine 2 1/2 cups orange juice and the apricots in a large nonaluminum saucepan; bring to a boil. Cover, reduce heat, and simmer 20 minutes or until apricots are tender.
Combine 1/4 cup orange juice and half of the apricot mixture in a blender or food processor, and process until smooth; pour into an extra-large bowl. Repeat procedure with remaining apricot mixture and 1/4 cup orange juice, except leave mixture in blender.
Sprinkle the gelatin over remaining 1 1/2 cups orange juice in a saucepan; let stand 1 minute. Cook over low heat 10 minutes, stirring until gelatin dissolves. Add gelatin mixture to apricot mixture in blender, and process until smooth. Add to the apricot mixture in bowl, stirring until well-blended. Place bowl over another extra-large bowl filled with ice; let stand until apricot mixture is chilled and thickened (about 30 minutes), stirring frequently and scraping sides of bowl. (If mixture sets up too much, whisk it until it becomes like pudding again.) Remove bowl from ice.
Combine egg whites (at room temperature), sugar, water, and corn syrup in an extra-large straight-sided bowl. Place bowl over simmering water in a large saucepan (water should not touch bottom of bowl). Beat egg white mixture at medium speed of a mixer 7 minutes. Increase speed to high; beat for 10 minutes or until mixture is smooth and satiny and stiff peaks begin to form. Remove bowl from simmering water; beat in vanilla.
Fold egg white mixture into apricot mixture; cover and chill at least 8 hours or up to 4 days.