Combine sliced strawberries, lime juice, sugar, and rum in a bowl. Let the berries mascerate in the juice, sugar, and rum for 20 minutes.
While the berries are mascerating, beat the cream and sugar until soft peaks form. Fold in the lime zest.
Place the angel food cake slices on a warm grill and toast all sides. Watch them carefully as they burn easily! Depending on the heat of your grill, toasting may take less than a minute per side.
Just before serving, toss the berries with the chopped mint. Serve a piece of grilled angel food cake with a large spoonful of berries and a good size dollop of whipped cream.