For pizza dough: Sprinkle the yeast and 1/4 teaspoon sugar over the warm water in a small bowl and let stand for 10 minutes or until the mixture is bubbly. Stir in 2 tablespoons of the olive oil. In a large bowl, combine the flour, remaining 1 teaspoon sugar, salt, and pepper. Add the yeast mixture to the flour mixture and stir with a wooden spoon to combine (the dough will be sticky).
Turn the dough out onto a lightly floured surface and knead until the dough is smooth and elastic. Using the nonstick spray, oil, or butter, lightly grease a large bowl. Place the dough into the prepared bowl, turning once to grease the surface of the dough. Cover and let rise in a warm place until double in size (45 to 60 minutes), or let rise overnight in the refrigerator.
For topping: While the dough is rising, combine the pizza sauce and barbecue sauce in a small bowl. Prep all the other ingredients for assembling the pizzas.
When the dough has risen, punch it down and then turn onto a lightly floured surface. Cut the dough into 4 equal portions. Cover and let rest for 15 minutes. Pat or roll each portion of dough into an 8-inch circle. For an easy transfer to the grill, place wax paper on a cookie sheet and sprinkle with the cornmeal. Place the dough rounds on the wax paper and brush the tops of the dough with the remaining 2 tablespoons of olive oil.
To assemble the pizzas, prepare a charcoal or gas grill for low-heat cooking and lightly grease the racks. Carefully place 2 of the dough circles, oiled-side down, onto the grill rack, directly over the low coals. Grill for about 6 minutes or until light brown and firm enough to transfer.
Transfer the crust, grilled-side up, to the back of the cookie sheet. Ladle one-fourth of the sauce on the grilled side of each of the crusts and top each with one-fourth of the pork, onion, peppers, and cheese. Carefully transfer the pizzas back to the grill and grill until the crust is crisp and the cheese melts, moving the pizzas as needed to cook evenly. Repeat with the remaining dough and toppings.