I think it would help to know what your current recipe is (in terms of ingredients and quantities) and the procedures you are following to make your dough. Although there are many factors that govern crust flavor, it is largely the result of the by-products of fermentation--which can be dramatically affected by the ingredients you are using, their quantities and the processing you are following. For example, too much yeast, or too much sugar, turbo-charged kneading (too fast), insufficient hydration (absorption of water by the flour), or temperatures that are too high, or a combination of these things, can foreshorten the duration of the fermentation process (it will spike up and come right back down quickly) and result in a reduction in the amount and intensity of the fermentation by-products, and hence the flavor of the crust. A long, slow fermentation, on the other hand, relying on a balance of ingredients (i.e., the ingredients are quantitatively within prescribed limits for the type of dough you are trying to make and are interjected into the process at the appropriate times), allows these fermentation by-products to more fully develop and intensify. In addition, there can also be a secondary fermentation due to natural yeasts to which the dough and its ingredients may be exposed, resulting in the more classical sourdough flavor that supplements the fermentation by-products produced from your regular dough production process. If you are letting your dough hang around the fridge for a week, I'm surprised that you aren't overwhelmed by flavor.
What you are asking also depends on what you mean by "sourdough". In common culinary parlance, the term "sourdough" encompasses not only doughs based on wild, or natural, yeasts, but also doughs based on starters that use commercial yeast. The former tends to produce unpredictable flavor results, since it depends on the natural yeasts captured from the air and in the flour to produce the starter for the dough (which may encompass hundreds of chemical and biological reactions), whereas the latter is based on a one-celled yeast, which lends itself to greater control. I have made doughs based on natural yeast starters and have not cared for the results. I have also made doughs using a starter based on commercial yeast and have found the results quite satisfying, with an abundance of flavor. The "faux" sourdough starter I used was based on simply mixing flour, water and yeast--basically a sponge or poolish--and letting it ferment and periodically feeding it with more flour so that it wouldn't expire. I'm sure that at some point, that starter was enhanced by natural yeast also. Offhand, I can't say that I can recall the use of sourdough starters, either natural or based on commercial yeast, for pizza doughs using high-gluten flour. I have made sourdough breads based on natural starters and high-gluten flour, and they were among the best breads I have ever eaten. Maybe others on this forum can speak with greater authority and experience than I on the extent to which pizza doughs can be made using starters and high-gluten flour.
I have set forth below a recipe for a dough that I have made using a starter based on a commercial yeast. I did not use the particular "sourdough" starter called for in the recipe, and I don't think you have to either. I used a simple starter based on flour, water and yeast, using considerably less yeast than called for in the recipe. I just made sure that the starter was adequately fed with flour, and, occasionally, a little bit of sugar. I could just as well have used a natural sourdough starter if it was of sufficient vigor. Whatever starter you use, you should experience the flavor enhancement that starters are known to produce.
I might also mention that Peter Reinhart, an expert on sougdough breads, also has a recipe for a soudough pizza dough in his book "American Pie", covering the entire process from making the natural starter to the finished dough. You may find it useful if you are interested in a true sourdough pizza dough.
"Sourdough" Pizza Dough Recipe
1 recipe "sourdough" starter (see recipe below)
4 1/4 to 4 1/2 c. all-purpose flour, unbleached
1 c. cold water
1 c. warm water (around 105-115 degrees F)
2 t. salt
For the "sourdough" starter:
2 c. skim-milk buttermilk
2 c. all-purpose flour, unbleached
1 packet active dry yeast (1T.)
1 T. sugar
To make the "sourdough" starter, in a 2-quart glass container that has been sterilized, stir together all the ingredients with a wooden spoon. Cover, with the lid slightly ajar, and let stand overnight in a warm place (75-80 degrees F), or until the starter bubbles and has a sour smell. (If the starter turns any color, or if mold appears on it, throw it out and try again.) Store, loosely covered, in the refrigerator, for up to 1 week.
Yield: Four cups.
To prepare the "sourdough" pizza dough, in a large nonaluminum bowl, stir together the "sourdough" starter, 1 cup of the all-purpose flour, and the cup of cold water. Cover with plastic wrap, and let stand at room temperature overnight.
In a large bowl, dissolve the salt in the cup of warm water. With a wooden spoon, stir in 1 cup of the sourdough mixture. (Return the remaining sourdough mixture to a clean container and refrigerate. It can be used as a sourdough starter for up to 1 week before replenishing again.) Gradually stir in enough of the remaining all-purpose flour to form a firm, soft dough. Turn the dough out onto a lightly floured surface and knead for 8 to 10 minutes, or until the dough is smooth and elastic, adding additional flour as needed to prevent the dough from sticking. Place the dough in a lightly oiled bowl, turn to coat, cover with plastic wrap, and let rise until doubled in bulk, about 2 hours. (The dough can be made ahead, punched down, enclosed in a large plastic bag and stored in the refrigerator for up to 2 days.)
Yield: 4 (12-inch) crusts or 8 (6-inch) crusts.