Preheat the oven to 350°F (175°C). Coat all 12 cavities of a jumbo muffin pan generously with nonstick cooking spray so the finished cakes can be released easily. Set the prepared pan aside.
Place the 4 room-temperature eggs in a large mixing bowl and whisk until uniformly smooth.
Add the granulated sugar, ¼ cup dark brown sugar, and 2 teaspoons rum or vanilla extract. Beat until the ingredients form a smooth, well-blended mixture.
Pour in the pineapple juice and stir until incorporated.
In a separate bowl, sift together the all-purpose flour, baking powder, cinnamon, ¼ teaspoon salt, and cornstarch.
Gradually incorporate the sifted dry mixture into the wet ingredients, whisking only until combined. Avoid excessive mixing. Set the completed batter aside while preparing the topping.
Melt the unsalted butter in a small saucepan over medium heat.
Stir in the 1½ cups dark brown sugar, 1 teaspoon rum, and ⅛ teaspoon salt. Whisk continuously and cook for 1 minute, until the mixture is glossy and evenly blended.
Remove the saucepan from the heat.
Immediately distribute approximately 2 tablespoons of the warm brown sugar mixture into the bottom of each prepared muffin cavity.
Position one drained pineapple ring over the topping in every cavity, then place one maraschino cherry in the center of each ring. Arrange the fruit promptly because the brown sugar mixture will become firmer as it cools.
Divide the prepared cake batter evenly among the 12 muffin cavities, spooning it over the pineapple and cherry layers. Fill each cavity to approximately three-quarters full.
Bake in the preheated oven for 20–22 minutes, or until the cakes are puffed and golden and a toothpick inserted into the center comes out clean. Monitor them carefully during the final few minutes because individual ovens can bake at slightly different rates.
Remove the muffin pan from the oven and allow the cakes to rest in the pan for 5 minutes.
Carefully run a knife around the perimeter of each cake to release any areas that may be sticking to the pan.
Position a wire cooling rack over the muffin tin, then securely invert the pan and rack together to release the cakes. The rack may be placed over a large sheet pan to catch any topping and simplify cleanup.
Serve the mini pineapple upside-down cakes while slightly warm or allow them to reach room temperature before serving.