Make the Syrup. Combine the 6 cups water, 6 ounces tamarind pulp, 1 cup sugar, and sliced ginger in a large saucepan. Bring to a boil over medium-high heat, stirring until the sugar dissolves. Lower the heat and simmer 5 minutes, breaking up the tamarind with the back of a spoon.
Quick Steep. Remove from heat and let it sit for 15-20 minutes.
Strain. Strain through a fine-mesh strainer into a punch bowl or large pitcher, pressing on the solids to get out as much liquid as possible. Discard the solids. The syrup can be made up to 3 days ahead and refrigerated if you want to get it out of the way early, but it's ready to use as soon as it cools to room temperature.
Add Rum and Ginger Beer. Right before serving, stir the 1 1/2 cups rum into the syrup, then pour in the can of ginger beer. Garnish with the lime slices and strawberry slices, reserving a few for individual glasses. Serve over ice.
Single Cocktail Version (makes 1 drink)
½ cup tamarind-ginger syrup (from above)
1½-2 ounces white rum
½ cup ginger beer, chilled
Ice
Lime slice and strawberry slice, for garnish
Fill a glass with ice, add the syrup and rum, and stir. Top with the ginger beer, give it one more gentle stir, and garnish with a lime and strawberry slice.