Pick crabmeat, removing any bits of shell. Whisk together lemon zest, next 2 ingredients, and 1 Tbsp. lemon juice. Fold in jalapeño pepper, next 2 ingredients, and crabmeat, using a rubber spatula. Season with kosher salt and freshly ground white pepper to taste.

Stir together peaches and remaining 4 Tbsp. lemon juice. Reserve 3 cups peach mixture. Pulse honey and remaining peach mixture in a food processor 8 to 10 times or until smooth. Season pureed peach mixture with kosher salt and freshly ground white pepper to taste.

Spoon 1/4 cup pureed peach mixture onto a chilled plate. Place a 3 1/2-inch round cutter in center of peach mixture on plate. (A clean, empty tuna can with both ends removed may be used instead.) Spoon one-sixth of diced avocados and 1/2 cup reserved chopped peach mixture into cutter, packing each layer firmly and sprinkling with kosher salt and freshly ground white pepper to taste. Top with about 1/2 cup crab mixture. Carefully remove cutter from plate. Repeat procedure with remaining pureed peach mixture, avocado, chopped peach mixture, and crab mixture. Arrange desired amount of arugula around each layered salad; serve immediately.