Put the chopped plums on a plate and freeze until completely frozen, at least 2 hours. Put 4 glasses in the freezer to chill.
Meanwhile, combine the ginger, sugar and pineapple juice in a small saucepan. Bring to a boil, then reduce the heat to low and simmer 5 minutes. Remove from the heat and let cool completely, then strain the syrup through a fine-mesh sieve into a small bowl, pressing on the solids.
Beat the heavy cream and coconut extract in a large bowl with a mixer on medium-high speed until stiff peaks form. Fold in the cream of coconut with a rubber spatula and refrigerate until ready to serve.
Puree the frozen plums, sake, plum wine, pineapple-ginger syrup and 1 cup ice in a blender until smooth and thick. Divide among the chilled glasses and top each with a thick layer of the coconut whipped cream. Garnish each with a pineapple and plum slice.