Prepare the remoulade sauce by whisking together all listed ingredients in a medium bowl until smooth; adjust seasoning to taste and refrigerate until serving. Slice the green tomatoes into 3/8-inch thick rounds with a serrated knife. Sprinkle both sides generously with coarse salt and allow them to rest for 30 minutes to extract excess moisture. Pat dry with paper towels. Arrange three shallow dishes: combine the flour, 1 & 1/2 teaspoons coarse salt, smoked paprika, garlic powder, onion powder, and black pepper in the first; whisk the buttermilk, egg white, and hot sauce in the second; mix the panko and cornmeal in the third. Position a wire rack over a rimmed baking sheet. Dredge each tomato slice in the flour mixture, shaking off excess, dip into the buttermilk mixture, then press into the panko-cornmeal blend to coat thoroughly. Place the coated slices on the wire rack and let stand briefly to set the crust. In a large cast iron skillet, heat the vegetable oil over medium-high until shimmering and at 350°F. Fry the tomatoes in batches of 3 to 4 slices, ensuring they are not crowded, cooking 3 to 5 minutes per side until golden and crisp, adjusting heat as needed. Transfer to a paper towel-lined plate to drain. Repeat with remaining slices, refreshing the oil if necessary. Serve immediately accompanied by the remoulade sauce.