Toss the romaine, iceberg, and half of the cilantro in a large bowl. In a blender or food processor, puree the chipotle chile and adobo sauce, sun-dried tomatoes, vinegar, brown sugar, and mustard. With the machine running, slowly pour in 1/2 cup of the oil. Transfer to a measuring cup; season to taste with salt and pepper.

In a shallow dish, mix the flour, cornmeal, chili powder, and cumin with 1 1/2 teaspoons salt and 1/2 teaspoon black pepper. Season the chicken with 1 teaspoon salt and then dredge in the flour mixture.

Heat 2 tablespoons of the remaining oil in a heavy nonstick skillet over medium-high heat until it's shimmering, about 1 minute. Add half of the chicken strips, evenly spaced, and cook without touching for 2 minutes. Flip and cook until the strips are just cooked through and firm to the touch, 1 to 2 minutes. Transfer to a large plate lined with paper towels and sprinkle with salt. Reduce the heat to medium, add the remaining 1 tablespoon oil, and cook the remaining strips in the same manner.

Discard the fat from the pan and wipe it clean with paper towels. Set the pan over low heat, add the vinaigrette, and cook, stirring with a wooden spoon or spatula, until warmed through, about 1 minute. Return the vinaigrette to a liquid measuring cup and whisk to recombine.

Gently toss the greens with about 14 cup of the vinaigrette or enough to lightly coat. Portion among four plates and top with the chicken, onion, avocado, corn, and the remaining 1/4 cup cilantro. Drizzle with some of the remaining vinaigrette (you may not need it all) and serve with lime wedges on the side for squeezing over the salads.