Lightly spoon flour into dry measuring cups; level with a knife. Combine 2 3/4 cups flour, sugar, yeast, and salt in a large bowl, stirring well with a whisk. Make a well in center of mixture. Combine water and oil; add to flour mixture. Stir until a soft dough forms. Turn the dough out onto a floured surface. Knead until smooth and elastic, about 10 minutes (dough will feel sticky), using enough of remaining flour, 1 tablespoon at a time, to keep hands from sticking.
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.)
Punch dough down. Divide dough into 5 equal portions. Shape each portion into a ball; cover and let rest 15 minutes. Working with one portion at a time (cover remaining dough to prevent drying), roll each portion into a 9-inch circle on a floured surface. Combine preserves and banana in a small bowl, stirring gently.
Working with 1 portion at a time, place dough on grill rack coated with cooking spray, and cook 2 minutes or until lightly browned. Turn dough, and top with about 1/3 cup apricot mixture. Spread mixture over dough, leaving a 1-inch border. Sprinkle about 1 1/2 tablespoons chocolate chips over apricot mixture. Repeat with remaining dough, apricot mixture, and chocolate chips. Cook 1 minute or until pizza is crisp. Cut into 4 wedges.