Add the flour, eggs, and panko breadcrumbs to three separate bowls. Dredge the avocado wedges in flour, shaking off the excess. Coat with egg and then panko, pressing to make sure it sticks.
In a deep, heavy-bottomed skillet, add 1 1/2 to 2 inches of vegetable oil. Heat over medium-high heat to 350°F. Working in batches, fry avocado until golden brown, approximately 1 to 2 minutes per side. Remove to a paper towel-line plate to drain. Season with salt.
In a small bowl, whisk together lime juice, mayonnaise, sour cream, chili powder, and cayenne pepper for the chili lime dressing.
To assemble tacos, divide avocado wedges evenly between the corn tortillas. Top with red cabbage, Monterey Jack cheese, and salsa verde. Drizzle with chili lime dressing and serve with lime wedges.