In a small bowl whisk together 3 tablespoons lime juice, the honey, brown sugar, chili powder, and cumin; set aside. With a sharp knife, score steak on both sides in a diamond pattern. Place steak in a dish; season both sides with salt and pepper. Brush half the sauce on both sides of the steak.
For a charcoal or gas grill, grill the steak on the rack of a covered grill directly over medium heat for 17 to 21 minutes (160 degrees F) or until desired doneness, turning and brushing with remaining sauce once. Brush corn with olive oil and place on grill rack next to steak. Grill for 15 to 20 minutes or until corn is tender and charred, turning occasionally to brown evenly. Remove steak and corn from grill rack. Let stand 10 minutes.
Meanwhile, for pico de gallo, in a medium bowl combine the tomatoes, cucumber, onion, cilantro, hot pepper sauce, 3 tablespoons lime juice, and 1/4 teaspoon salt. Cut the corn kernels from the cobs. Add to tomato mixture along with avocado. Stir gently to combine.
To serve, thinly slice steak against the grain. Top with the pico de gallo.