Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high.
To make the caramelized onions, combine the onion, pepper sauce, broth, vinegar, oil, garlic, and brown sugar in a 10-inch nonstick, fire-proof skillet, cover with a lid, and place on the grill rack. Cook the onion mixture for 15 to 20 minutes, stirring occasionally, until the onions are caramelized and most of the liquid is evaporated. Remove the pan from the grill and set aside.
To make the spread, combine the cheeses in a fire-proof saucepan, cover, and set aside.
To make the patties, combine the chuck, sirloin, onion, Zinfandel, herbs, pepper sauce, and seasoned salt in a large bowl. Handling the meat as little as possible to avoid compacting it, mix well. Divide the mixture into 6 equal portions and form the portions into patties to fit the rolls.
When the grill is ready, brush the grill rack with vegetable oil. Place the patties on the rack, cover, and cook, turning once, until done to preference, 5 to 7 minutes on each side for medium. Meanwhile, place the saucepan with the cheese spread on the outer edge of the rack to warm the cheese mixture just until it reaches a very soft, spreading consistency. Remove the saucepan from the grill and set aside.
During the final minutes of grilling the patties, brush the avocado slices with balsamic vinegar and sprinkle with seasoned salt. Arrange on a rimmed nonstick perforated grilling pan coated lightly with oil and grill alongside the patties for 1 to 2 minutes, turning as necessary. During the final 30 seconds, add the bacon slices to the pan. When the avocados are nicely grilled and the bacon is crisp, remove from the grill. When the patties are cooked, remove from the grill, stacking to keep warm. Place the rolls, cut side down, on the outer edges of the grill rack to toast lightly.
To assemble the burgers, spread a generous amount of the cheese mixture over the cut sides of the rolls. On each roll bottom, place a lettuce leaf, a tomato slice, a patty, an equal portion of the caramelized onions, 2 avocado slices, and 2 bacon slices. Add the roll tops and serve.