Combine blackberries, ketchup, blackberry jelly, sugar, raspberry balsamic vinegar, corn syrup, tomato paste, limeade concentrate, cider vinegar, salt, bourbon, garlic powder, liquid smoke, ginger, ground chipotle pepper, red pepper flakes, black pepper, teriyaki sauce, and hot pepper sauce in a large pot and bring to a simmer over medium-high heat.
Reduce heat to medium-low and simmer blackberry mixture for 10 minutes. Add whole habanero peppers and continue to simmer until sauce is thickened, about 20 minutes more. Remove and discard habanero peppers.
Pour barbecue sauce into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth.