Unfold crust and press out fold lines. Sprinkle with flour. Roll out to 12 1/2-inch round. Arrange floured side down in 11-inch-diameter tart pan with removable bottom. Pierce bottom and sides with fork.
Bake until golden brown, about 12 minutes. Check crust during baking; if sides of crust slide down, press up with back of fork. Cool completely.
Using electric mixer, beat cream cheese until smooth. Mix in cream of coconut and sugar, then 3/4 cup coconut and ginger. Spread filling in crust.
Arrange papaya attractively atop filling.
Melt preserves in heavy small saucepan over low heat, stirring frequently. Brush over papaya. Sprinkle remaining 1/4 cup toasted coconut around edge of tart and in center.
Refrigerate until filling is firm, at least 1 hour. (Can be prepared 6 hours ahead. Keep refrigerated.)