I can consistently make a nice, well-blistered, chewy pizza crust in my wood-fired oven. My recipe is Caputo flour (the red bag), 60% hydration, 2.5% salt, 0.25% instant yeast; knead until smooth; form into balls; age at 9 C for four days. I've tried to expand into sourdough, and I can't get satisfactory results. My best approach has been to use the starter (also at 60% hydration, doubled every day and kept at room temperature) for 1/4 of the dough volume. This produces a reasonably okay dough, but without much sour tang, and with less elasticity (difficult to keep the thickness consistent, and stretches out of shape when pulled onto the peel). I've also tried fermenting at 35 C initially and reducing the fermentation time, as well as a long ferment at 100% hydration and adding flour to bring it down to 60% hydration an hour before forming. In all cases, whenever the dough develops significant sourness, it also becomes completely unworkable for forming and transferring to the oven floor. I assume that the acidity is simply destroying the gluten structure, which wouldn't be a big problem in a pan but is impractical for baking on the oven floor. Any secret technique, for getting a pronounced sourdough taste in a pizza crust without it turning into goo? 
I have the same experience. Did you try using a preferment that is half yeast preferment and half sourdough preferment? It is a technique used in Tartine and I have had some promising results with this. 