Heat the olive oil in a large deep skillet over medium-high heat until shimmering.
Add the chopped onion and sauté until tender, about 5 minutes.
Add the minced garlic and cook, stirring, for about 30 seconds until fragrant.
Pour in 3 cups of the bottled clam juice, then add the drained hominy, salsa verde, sun-dried tomatoes, and grated lime peel; bring to a simmer and cook 5 minutes.
If preparing ahead: cool slightly, refrigerate uncovered until cold, then cover and chill for up to 4 hours; bring back to a simmer before continuing.
Add the mixed seafood and 3 tablespoons of the chopped cilantro to the simmering broth; add more clam juice if you want a thinner broth.
Simmer until the seafood is just opaque in the center, about 3 minutes; do not overcook.
Season to taste with salt and pepper, divide among bowls, and sprinkle with the remaining tablespoon of cilantro.