Start charcoal fire or preheat gas grill to medium–high heat.
Combine 2 cups flour, undissolved yeast, sugar and salt in a large bowl. Add very warm water and oil; mix until well blended, about 1 minute. Gradually add enough remaining flour to make a soft dough. Dough should form a ball and will be slightly sticky. Knead** on a floured surface, adding additional flour if necessary, until smooth and elastic, about 5 minutes.
Divide dough into 8 portions. Pat or roll dough on a well–floured counter to about 8–inch/20–cm circles; they do not need to be perfect.
Using hands, lift each crust carefully and place on grill. Cook for 3 to 4 minutes until bottom is lightly browned and top looks set. Using long handled tongs, remove crust from grill, grilled side up, to a platter or baking sheet.
Spread 1 tablespoon Alfredo sauce over the grilled side of each pizza crust. Top with shrimp, 1 tablespoon green onions and 1–1/2 teaspoons red bell pepper. Sprinkle 1/4 cup cheese over top. Repeat with remaining pizzas.
Carefully slide each pizza onto the grill. Cook an additional 3 to 4 minutes until bottom of crust is browned and cheese is melted. Remove from grill and serve immediately.
*If you don't have a thermometer, water should feel very warm to the touch.
**To knead the dough, add just enough flour to the dough and your hands to keep the dough from sticking. Flatten dough and fold it toward you. Using the heels of your hands, push the dough away with a rolling motion. Rotate dough a quarter turn and repeat the fold, push and turn steps. Keep kneading dough until it is smooth and elastic. Use a little more flour if dough becomes too sticky, always working the flour into the ball of dough.
Make Ahead: Dough (but NOT individual crusts) may be made up to 24 hours in advance and stored covered in the refrigerator. Punch down and roll out just before grilling. OR, pizzas may be partially grilled ahead of serving. Here's how: Grill one side of the pizza crust. Cool. Tightly wrap and refrigerate until serving time. Top pizzas with desired toppings (on grilled side) and finish grilling on preheated grill.
Dough sticking to grill? Make sure grill has been preheated and cleaned. To prevent sticking, drizzle oil over paper towel and carefully wipe over grates.