Fill a large bar shaker with ice. Add the lime wedges and rum and crush together with a muddler or wooden spoon. Add the Triple Sec, simple syrup, and lime juice and shake well. Strain into shot glasses and serve as part of the trio.
In a small saucepan, stir sugar into water. Cook over low heat until the sugar has dissolved, about 5 minutes. Let cool and store in an airtight container in the refrigerator for up to 2 weeks.
Fill a heavy Dutch oven a little less than halfway with oil. Heat oil to 360 degrees F.
Crack the eggs into a medium bowl. With a whisk, lightly beat the eggs and pour in the cold soda water. Slowly incorporate the flour into the egg mixture and continuing to whisk until a smooth batter forms. Season the batter with salt and pepper. Pat the shrimp dry with a paper towel. Dip the shrimp into the batter allowing the excess batter to drip off. Fry the shrimp in the heated oil until golden brown and just cooked within, about 4 minutes. Remove to a paper towel lined plate to drain. Serve immediately as part of the trio with the Miami Mojo.