Whisk 2 tbsp. lime juice with olive oil, tequila, cilantro, 1/2 tsp. salt, and the pepper in a bowl. Add oysters and their juices, reserving bottom shells. Chill oysters 30 to 45 minutes and then drain, reserving about 1 1/2 cups marinade.
Meanwhile, soak shells in water for 30 minutes. Drain on a kitchen towel and pat dry. Preheat gas or charcoal grill to very hot (you can hold your hand 1 to 2 in. above the grill only 1 to 2 seconds).
In a small bowl, whisk together butter, mayonnaise, chile and sauce, lime zest, remaining 2 tsp. lime juice, and remaining 1/2 tsp. salt. Set glaze aside.
Spread rock salt over the bottom of a platter large enough to hold oysters in a single layer. Arrange oyster shells on a large baking pan and spray insides lightly with cooking spray.
Position half of the shells on the grill (place between the bars so they won't roll over). Heat shells 30 seconds. Spoon 1 oyster into each shell with 1 tbsp. marinade and cook (close lid on gas grill) until juices are bubbling, 2 to 3 minutes. Drizzle a teaspoon of glaze onto each oyster and cook 30 seconds more. Using tongs, carefully transfer oysters to platter and nestle them into the salt. Grill remaining oysters the same way. Serve immediately.
Note: Nutritional analysis is per serving.