Preheat oven to 425°F. Line a 12-cup muffin tray using paper liners.

Process 1 ¼ cups diced strawberries in a blender until smooth, 15 to 30 seconds. Pour ⅔ cup blended strawberry mixture into a small bowl; whisk in 2 ½ tablespoons rum until well combined. Set aside. Reserve remaining 1 tablespoon strawberry-rum mixture for the glaze.

Beat ¾ cup granulated sugar, 10 tablespoons butter, and lime zest in a large bowl with an electric mixer on medium until fluffy, 3 to 4 minutes, stopping to scrape down sides of bowl as needed. Add eggs, 1 at a time, beating until combined after each addition, about 30 seconds to 1 minute.

Whisk together flour, baking powder, salt, and freeze-dried strawberries in a medium bowl.

Stir flour mixture into butter mixture, alternating with strawberry-rum mixture until nearly combined but pockets of flour remain. Fold remaining ½ cup chopped strawberries into batter just until combined. (Do not overmix.)

Pour batter evenly into prepared muffin wells (about a scant ⅓ cup each), spreading into an even layer. Sprinkle evenly with remaining 2 tablespoons granulated sugar (about ½ teaspoon per well).

Bake the cupcakes for 5 minutes. Reduce oven temperature to 375°F, and continue baking until a wooden pick inserted into center of muffins comes out clean, 10 to 12 minutes. Let cool in muffin tray 10 minutes. Remove muffins from tray, and place on a wire rack placed over a rimmed baking sheet.

Microwave remaining 2 tablespoons butter in a medium bowl on HIGH until melted, about 30 seconds; stir in powdered sugar, lime juice, and remaining 1 tablespoon rum and 1 tablespoon reserved strawberry-rum mixture until combined. Gradually add additional lime juice, ½ to 1 teaspoon at a time as needed, until desired consistency is reached. Drizzle glaze over muffins. Garnish with lime zest and lime slices. Serve warm, or let cool until room temperature, about 45 minutes.