There are people here with more experience than me, but I'd say you are adding too much flour AND not keading the dough enough. If the dough has enough gluten and has had time to relax, it should be easy to stretch the dough.
I personally only add enough flour to make the dough workable, if it feels really smooth then I think there is too much flour.
There is a great forum dedicated 100% to pizza making. PizzaMaking.com - Pizza Making, Pizza Recipes, and More!
They have great advice and great recipes. I found one on there that is my favorite. Easy to make and tastes amazing:
Little Caesars Pizza Dough
1 1/4 (9.7 oz) warm water (appox. 120° F)
2 3/4 tsp. dry active yeast
2 TBSP sugar
1 TBSP Honey
1 TBSP Olive Oil
2 Tsp. Salt
1 1/2 cups (8 oz.) bread flour or all purpose flour
1 1/2 cups (8 oz.) whole wheat flour (optional, can use 100% bread flour or all purpose flour)
Mix water and yeast in mixing bowl and allow it to proof for 5 minutes. Mix in sugar, honey and oil. Then mix in 1 cup flour and the salt. Continue mixing in all the remaining flour until you get a nice, soft dough. Knead until dough is soft and smooth (approx. 10 minutes).
Finish kneading on a lightly floured surface and shape into a ball. Place in the refrigerator in a covered container coated with olive oil for overnight (or make this dough first thing in the morning and place in the fridge until dinner that evening).
3 hours before baking: Remove from fridge and either divide dough in half for two 12” pizzas or leave whole for one somewhat thicker 16” pizza. Work each piece of dough into balls. Allow the dough to come back to room temperature (this process generally takes 3 hours).
45 minutes before baking: With your pizza stone on the bottom rack of your oven, preheat your oven to 475° F to allow the stone to get hot enough (this process generally takes 40-50 minutes).
15 minutes before baking: Shape dough into desired pizza crust, sprinkle pizza peel, wooden cutting board or upside down cookie sheet with corn meal, flour or rice flour. Place pizza crust on top, then add toppings. Gently slide pizza onto the hot pizza stone and bake for 9-11 minutes.
I’ve spent some time on the Pizzamaking forum where there are several dozen amazing chef’s who have dedicated an extraordinary amount of time perfecting pizza making at home. Some of their doughs take up to 7 days to make with a huge focus on temperature control and top quality ingredients. They are inspiring!
This recipe is from their site but is simple to use, forgiving and only takes a day to make without sacrificing on the flavor. It was designed to mimic the flavor of Little Caesars pizza using the same processing time as the restaurant along with the same cornerstone ingredients.
After trying this recipe, we no longer crave takeout pizza- this is SO much better (at least we think so)! Yeah!!!
I think the two secrets to great homemade pizza are finding the right dough and baking it on a hot stone (Fibrament sells a great stone with an outstanding reputation and a 10 year warranty against cracking). The benefit of baking it on a hot stone is it duplicates the professional brick ovens. The ceramic stone creates a light crispy crust by absorbing excess moisture and distributing the heat evenly and efficiently. The results are night and day compared to baking a pizza on a cookie sheet or cold stone. Give it a try, you’ll love it!
Thanks to Randy at the Pizzamaking forum for providing this excellent recipe!