Stir together mayonnaise and 1/2 teaspoon garlic in a small bowl. Spread 1 tablespoon of the mayonnaise mixture evenly over 1 side of each bread slice.
Stir together cream cheese, scallions, bacon, 1 1/2 cups Cheddar cheese, and remaining 1/2 teaspoon garlic in a bowl until well combined. Spread mixture evenly over bare sides of 4 of the bread slices (about heaping 1/2 cup each); top evenly with American cheese, overlapping as needed to fit. Top with remaining 4 bread slices, mayonnaise side up.
Sprinkle 6 tablespoons Cheddar cheese evenly on the bottom of a nonstick skillet. Place 1 assembled sandwich on top of Cheddar in the skillet. Cook over medium-low, undisturbed, until cheese is browned and crispy on underside, 4 to 6 minutes. Flip and cook, undisturbed, until mayonnaise side is browned, 2 to 3 minutes.
Transfer sandwich to a wire rack set in a large rimmed baking sheet, Cheddar-side up. Repeat process with remaining Cheddar and sandwiches. Slice sandwiches in half diagonally before serving.
