Pour water into a large bowl. Sprinkle with yeast. Let stand until dissolved, about 5 minutes.
Add 3 cups flour and 2 teaspoons salt and stir until smooth. Add another 2 cups flour and stir until smooth.
Continue adding flour (up to 1/2 cup), 1 tablespoon at a time, stirring, until dough comes away from sides of bowl but is still sticky.
Turn dough out onto a lightly floured surface. Knead dough with floured hands: Throw it down on surface, pulling it toward you with 1 hand and pushing it away from you with the other. Fold dough back over itself (use a dough scraper or a wide knife to scrape dough from surface), and knead until smooth, elastic, and soft but still a little tacky, about 10 minutes.
Shape dough into a ball, and transfer to a lightly oiled bowl; turn to coat. Cover with plastic wrap and let stand in a warm place until doubled in volume, about 3 hours.
Heat grill to high. Scrape dough out of bowl onto a lightly floured surface and cut into 6 equal pieces. Shape each piece into a ball.
Dust with flour, and cover with plastic wrap. Let stand until dough is almost doubled in volume, 20 to 30 minutes.
Holding top edge of 1 dough ball in both hands, let bottom edge touch surface (refrigerate remaining balls as you work).
Carefully move hands around edge to form a circle, as if turning a wheel. Hold dough on back of your hand, letting its weight stretch it into a 12-inch round.
Transfer dough to a lightly floured pizza peel (or an inverted baking sheet). Press out edges using your fingers. Lightly jerk peel; if dough sticks, lift, and dust more flour underneath.
Heat grill to high. Grill pizza dough, flipping occasionally, until charred and cooked through, about 4 minutes.
Cook bacon in a large pot over medium-low heat until fat is rendered, and bacon is crisp, about 10 minutes. Transfer bacon to a plate using a slotted spoon.
Add oil, garlic, and onion to pot. Cook, stirring occasionally, until softened, about 4 minutes.
Add wine and clams. Bring to a simmer. Cook, covered, until clams open, about 5 minutes. Transfer clams to a plate using a slotted spoon. Discard any unopened clams. Remove remaining clams from shells.
Strain cooking liquid through a fine sieve and return to pot. Add cream and cook over medium heat until thick and reduced to 1 cup, about 10 minutes. Add red-pepper flakes.
Preheat oven to 400 degrees (or heat grill to medium). Spoon 1/3 cup sauce over each grilled pizza crust. Top with reserved clams and bacon. Bake or grill, covered with lid, directly on grates, until sauce is bubbling, 5 to 7 minutes (time may vary slightly if grilling).
Remove from oven or grill. Top with parsley, and drizzle with oil.