To prepare berries, combine first 5 ingredients; toss to combine. Cover and chill 1 hour.
Preheat oven to 375°.
To prepare cake, place a rack in the lower third of oven. Lightly spoon flour into a dry measuring cup; level with a knife. Sift together flour, 1/2 cup powdered sugar, and ginger in a medium bowl. Sift together remaining 1/2 cup powdered sugar and 3/4 cup granulated sugar in another bowl. Place egg whites in a large bowl; beat with a mixer at high speed until foamy. Add cream of tartar and salt; beat until soft peaks form. Add powdered and granulated sugar mixture, 1 tablespoon at a time, beating until stiff peaks form. Sift flour mixture over egg white mixture, 1/4 cup at a time; fold in. Fold in 2 tablespoons juice.
Spoon batter into an ungreased 10-inch tube pan, spreading evenly. Break air pockets by cutting through batter with a knife. Bake at 375° for 30 minutes or until cake springs back when lightly touched. Invert pan; cool completely. Loosen cake from sides of pan using a narrow metal spatula. Invert the cake onto a plate.
Cut 1 inch off top of cake using a serrated knife; set top of cake aside. Hollow out bottom of cake using a small knife, leaving a 1-inch-thick shell; reserve torn cake for another use.
To prepare whipped cream, place cream in a medium bowl; beat with a mixer at high speed until soft peaks form. Scrape seeds from vanilla bean into bowl; discard pod. Gradually add 3/4 cup powdered sugar, beating at high speed until stiff peaks form.
Spoon all but 1 cup of berry mixture into cake shell; top with whipped cream. Replace top of cake; sprinkle with 2 tablespoons powdered sugar. Serve immediately with additional berry mixture; garnish with orange rind, if desired.