Place the pineapple in a plastic container in the freezer until completely frozen, at least 3 hours. In a blender, combine 1 1/2 cups spiked watermelon, 6 tablespoons frozen pineapple, and 1/2 cup Citrus-Ginger Infusion. (Amount of infusion may be increased or decreased according to individual taste.) Blend on high speed until well combined. Add enough ice to fill the blender, 3 cups, and additional vodka, as desired, and blend until smooth. Pour into tall chilled glasses or a pitcher. Repeat with the remaining ingredients, to make about 10 blenderfuls. Garnish with mint sprigs and serve with a long straw.
Cut a hole in the top of the watermelon, wide and deep enough to insert a funnel. Pour in as much vodka through the funnel as can be absorbed (1/2 to 1 cup). Remove the funnel and replace the watermelon plug. Let sit for 4 hours.
Again, pour in as much vodka as can be absorbed. Repeat the process until all the vodka has been absorbed. (The watermelon flesh gradually will absorb all the vodka.) Refrigerate until well chilled. When ready to make the daiquiris, cut the watermelon in half and scoop out the flesh.
Combine the water, sugar, lemon grass, ginger, and lemon juice and zest in large saucepan. Bring to a boil, stirring until the sugar dissolves. Remove from the heat and let cool.
Strain through a fine mesh sieve into a clean container and reserve for the daiquiris. (Infusion will keep for 2 weeks, refrigerated and also may be used to flavor dressings or drizzle over fresh fruit.)