Pour 3/4 cup warm water in the bowl of a stand mixer with dough hook attached. Weigh or lightly spoon flour into dry measuring cups and spoons; level with a knife. Add flour to 3/4 cup water; mix until combined. Cover and let stand 20 minutes. Combine remaining 1/4 cup water and yeast in a small bowl; let stand 5 minutes or until bubbly. Add yeast mixture, 4 teaspoons oil, and salt to flour mixture; mix 5 minutes or until a soft dough forms. Place dough in a large bowl coated with cooking spray; cover surface of dough with plastic wrap lightly coated with cooking spray. Refrigerate 24 hours.
Remove dough from refrigerator. Let stand, covered, 1 hour or until dough comes to room temperature. Punch dough down. Press dough out to a 12-inch circle on a lightly floured baking sheet, without raised sides, sprinkled with cornmeal. Crimp edges to form a 1/2-inch border. Cover dough loosely with plastic wrap.
Prepare grill to high.
Heat a Dutch oven over medium-high heat. Add remaining 2 tablespoons oil to pan; swirl to coat. Add butter; swirl until butter melts. Add shallots; sauté 2 minutes. Add garlic; sauté 1 minute. Stir in wine and clams; bring to a boil. Cover and cook 8 minutes or until shells open; discard any unopened shells. Remove clams from pan using a slotted spoon. Strain cooking liquid through a fine sieve over a bowl, reserving solids. Reserve cooking liquid for another use. Remove clams from shells; discard shells. Chop clams; toss with reserved solids.
Place pizza dough, cornmeal side up, on grill rack coated with cooking spray; grill 4 minutes or until blistered. Turn dough over; grill 3 minutes. Remove from grill. Spread clam mixture evenly over top side of crust, leaving a 1/2-inch border; top with cheese. Return pizza to grill rack; grill 4 minutes or until thoroughly cooked. Remove from grill. Sprinkle with parsley and oregano. Cut pizza into 10 wedges.