Place lime pieces in a 12-ounce glass and top with mint leaves and cane sugar. Using a muddler, crush the lime pieces while bruising the mint with the sugar. Fill the glass just below the rim with the ice. Add the mint syrup, coconut milk, pineapple juice, pineapple rum and the coconut rum. Use a shaker to vigorously shake the contents of the glass together for at least 30 seconds. Pour the mojito back in the glass, and top off the glass with seltzer water. Place a sugar cane stick in each glass and garnish with fresh mint leaves. Serve immediately.
Place the sugar and the water in a small saucepan. Bring to a gentle boil over medium-low heat, stirring occasionally to help dissolve the sugar. While the syrup heats, rinse the mint leaves to eliminate any dirt. Once the sugar has dissolved, remove the syrup from the heat, and dump the mint leaves into the saucepan. Allow the syrup to cool for at least 1 hour before straining out the mint. Store the syrup in an airtight container and place in the refrigerator until ready to use. Syrup will keep, refrigerated, for several weeks.