Pulse shrimp in food processor until finely ground. Scrape down sides and add cream. Pulse a few more times to a fine puree.
Combine crab, shrimp mousse, herbs, lemon balsamic, and 1 egg in a large bowl and fold gently with a spatula until combined, being careful not to break up the large lumps of crab. Divide mixture into 8 balls and firmly press into 1/2-inch-thick disks. Place cakes on rimmed baking sheet lined with parchment paper, cover tightly with plastic wrap, and refrigerate for 30 minutes.
Place remaining egg in a small bowl and beat thoroughly. Mix bread crumbs and seasoning in a second small bowl. Working one crab cake at a time, dip in egg, then in bread crumbs, pressing down gently to adhere. Return to baking sheet, and repeat with remaining disks.
Meanwhile, poach eggs: Bring water, salt and vinegar to a boil in a large, high side sauté pan. Reduce heat to maintain a low simmer. Crack 1 egg into a glass measuring cup, hold spout close to water's surface, and let egg slip gently into water. Repeat with rest of eggs. Cook until eggs are softly set, 2 to 3 minutes, flip eggs and cook 30 more seconds. Using a slotted spoon, transfer as done to a large bowl of ice and cold water.
Heat 1 tablespoon oil in a skillet over medium heat until shimmering. Place 4 cakes in skillet and cook without moving them until golden brown, 3 to 4 minutes. Using 2 spatulas, carefully flip cakes, add 1 tablespoon oil, reduce heat to medium-low, and continue to cook until second side is golden brown, 4 to 6 minutes. Transfer to a plate and put in a 200° oven to keep warm. Wipe out skillet and repeat with remaining 4 cakes and remaining 2 tablespoons oil.