Pound swordfish very carefully to no more than 1/8-inch thick. Season the fish with salt and pepper.
Pour breadcrumbs into a shallow dish. Finely chop the parsley and the crumbs along with the zests, chili flakes and garlic to the pile of parsley then chop together to combine. Work the gremolata through the breadcrumbs evenly then season with salt.
Arrange the eggplant on kitchen towel, salt it and let drain for 20 minutes. Press out excess liquids.
For the caponata, heat a large deep skillet over medium high heat with EVOO, 3 turns of the pan. Add eggplant, celery, onions, olives, chili flakes and garlic, and season with salt and pepper. Cook partially covered to soften, 7-8 minutes, then add pine nuts and tomatoes. Reduce heat, simmer 10 minutes more to just tender then stir in torn basil.
Heat a shallow layer of olive oil in very large skillet. Press cutlets firmly into the breadcrumbs to coat then cook cutlets to golden on each side in small batches of 2 to 3 at a time. Keep cooked cutlets warm in oven preheated to 275°F on rack-lined baking sheet.
Serve cutlets with lemon wedges and caponata alongside.